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Simplifying 15(2x + 6) + 3(x + -4)(x + 4) = 3x * 3x + 2 + -5(4x + 2) Reorder the terms: 15(6 + 2x) + 3(x + -4)(x + 4) = 3x * 3x + 2 + -5(4x + 2) (6 * 15 + 2x * 15) + 3(x + -4)(x + 4) = 3x * 3x + 2 + -5(4x + 2) (90 + 30x) + 3(x + -4)(x + 4) = 3x * 3x + 2 + -5(4x + 2) Reorder the terms: 90 + 30x + 3(-4 + x)(x + 4) = 3x * 3x + 2 + -5(4x + 2) Reorder the terms: 90 + 30x + 3(-4 + x)(4 + x) = 3x * 3x + 2 + -5(4x + 2) Multiply (-4 + x) * (4 + x) 90 + 30x + 3(-4(4 + x) + x(4 + x)) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + 3((4 * -4 + x * -4) + x(4 + x)) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + 3((-16 + -4x) + x(4 + x)) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + 3(-16 + -4x + (4 * x + x * x)) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + 3(-16 + -4x + (4x + x2)) = 3x * 3x + 2 + -5(4x + 2) Combine like terms: -4x + 4x = 0 90 + 30x + 3(-16 + 0 + x2) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + 3(-16 + x2) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + (-16 * 3 + x2 * 3) = 3x * 3x + 2 + -5(4x + 2) 90 + 30x + (-48 + 3x2) = 3x * 3x + 2 + -5(4x + 2) Reorder the terms: 90 + -48 + 30x + 3x2 = 3x * 3x + 2 + -5(4x + 2) Combine like terms: 90 + -48 = 42 42 + 30x + 3x2 = 3x * 3x + 2 + -5(4x + 2) Reorder the terms for easier multiplication: 42 + 30x + 3x2 = 3 * 3x * x + 2 + -5(4x + 2) Multiply 3 * 3 42 + 30x + 3x2 = 9x * x + 2 + -5(4x + 2) Multiply x * x 42 + 30x + 3x2 = 9x2 + 2 + -5(4x + 2) Reorder the terms: 42 + 30x + 3x2 = 9x2 + 2 + -5(2 + 4x) 42 + 30x + 3x2 = 9x2 + 2 + (2 * -5 + 4x * -5) 42 + 30x + 3x2 = 9x2 + 2 + (-10 + -20x) Reorder the terms: 42 + 30x + 3x2 = 2 + -10 + -20x + 9x2 Combine like terms: 2 + -10 = -8 42 + 30x + 3x2 = -8 + -20x + 9x2 Solving 42 + 30x + 3x2 = -8 + -20x + 9x2 Solving for variable 'x'. Reorder the terms: 42 + 8 + 30x + 20x + 3x2 + -9x2 = -8 + -20x + 9x2 + 8 + 20x + -9x2 Combine like terms: 42 + 8 = 50 50 + 30x + 20x + 3x2 + -9x2 = -8 + -20x + 9x2 + 8 + 20x + -9x2 Combine like terms: 30x + 20x = 50x 50 + 50x + 3x2 + -9x2 = -8 + -20x + 9x2 + 8 + 20x + -9x2 Combine like terms: 3x2 + -9x2 = -6x2 50 + 50x + -6x2 = -8 + -20x + 9x2 + 8 + 20x + -9x2 Reorder the terms: 50 + 50x + -6x2 = -8 + 8 + -20x + 20x + 9x2 + -9x2 Combine like terms: -8 + 8 = 0 50 + 50x + -6x2 = 0 + -20x + 20x + 9x2 + -9x2 50 + 50x + -6x2 = -20x + 20x + 9x2 + -9x2 Combine like terms: -20x + 20x = 0 50 + 50x + -6x2 = 0 + 9x2 + -9x2 50 + 50x + -6x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 50 + 50x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 25x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 25x + -3x2)' equal to zero and attempt to solve: Simplifying 25 + 25x + -3x2 = 0 Solving 25 + 25x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -8.333333333 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -8.333333333x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -8.333333333x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -8.333333333x + x2 = 0 + 8.333333333 -8.333333333x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -8.333333333x + x2 = 8.333333333 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = 8.333333333 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = 8.333333333 + 17.36111111 Combine like terms: 8.333333333 + 17.36111111 = 25.694444443 17.36111111 + -8.333333333x + x2 = 25.694444443 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 25.694444443 Calculate the square root of the right side: 5.068968775 Break this problem into two subproblems by setting (x + -4.166666667) equal to 5.068968775 and -5.068968775.Subproblem 1
x + -4.166666667 = 5.068968775 Simplifying x + -4.166666667 = 5.068968775 Reorder the terms: -4.166666667 + x = 5.068968775 Solving -4.166666667 + x = 5.068968775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 5.068968775 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 5.068968775 + 4.166666667 x = 5.068968775 + 4.166666667 Combine like terms: 5.068968775 + 4.166666667 = 9.235635442 x = 9.235635442 Simplifying x = 9.235635442Subproblem 2
x + -4.166666667 = -5.068968775 Simplifying x + -4.166666667 = -5.068968775 Reorder the terms: -4.166666667 + x = -5.068968775 Solving -4.166666667 + x = -5.068968775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -5.068968775 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -5.068968775 + 4.166666667 x = -5.068968775 + 4.166666667 Combine like terms: -5.068968775 + 4.166666667 = -0.902302108 x = -0.902302108 Simplifying x = -0.902302108Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.235635442, -0.902302108}Solution
x = {9.235635442, -0.902302108}
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