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Simplifying 3x(x + 9) = 2(x + 2) + x + -7 Reorder the terms: 3x(9 + x) = 2(x + 2) + x + -7 (9 * 3x + x * 3x) = 2(x + 2) + x + -7 (27x + 3x2) = 2(x + 2) + x + -7 Reorder the terms: 27x + 3x2 = 2(2 + x) + x + -7 27x + 3x2 = (2 * 2 + x * 2) + x + -7 27x + 3x2 = (4 + 2x) + x + -7 Reorder the terms: 27x + 3x2 = 4 + -7 + 2x + x Combine like terms: 4 + -7 = -3 27x + 3x2 = -3 + 2x + x Combine like terms: 2x + x = 3x 27x + 3x2 = -3 + 3x Solving 27x + 3x2 = -3 + 3x Solving for variable 'x'. Reorder the terms: 3 + 27x + -3x + 3x2 = -3 + 3x + 3 + -3x Combine like terms: 27x + -3x = 24x 3 + 24x + 3x2 = -3 + 3x + 3 + -3x Reorder the terms: 3 + 24x + 3x2 = -3 + 3 + 3x + -3x Combine like terms: -3 + 3 = 0 3 + 24x + 3x2 = 0 + 3x + -3x 3 + 24x + 3x2 = 3x + -3x Combine like terms: 3x + -3x = 0 3 + 24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 8x + x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + x2 = 0 Solving 1 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x + x2 = 0 + -1 8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 8x + x2 = -1 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -1 + 16 Reorder the terms: 16 + 8x + x2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + 8x + x2 = 15 Factor a perfect square on the left side: (x + 4)(x + 4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 4) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 4 = 3.872983346 Simplifying x + 4 = 3.872983346 Reorder the terms: 4 + x = 3.872983346 Solving 4 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.872983346 + -4 x = 3.872983346 + -4 Combine like terms: 3.872983346 + -4 = -0.127016654 x = -0.127016654 Simplifying x = -0.127016654Subproblem 2
x + 4 = -3.872983346 Simplifying x + 4 = -3.872983346 Reorder the terms: 4 + x = -3.872983346 Solving 4 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.872983346 + -4 x = -3.872983346 + -4 Combine like terms: -3.872983346 + -4 = -7.872983346 x = -7.872983346 Simplifying x = -7.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.127016654, -7.872983346}Solution
x = {-0.127016654, -7.872983346}
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