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Simplifying 4(x + 8) = 3(x + -9) * x Reorder the terms: 4(8 + x) = 3(x + -9) * x (8 * 4 + x * 4) = 3(x + -9) * x (32 + 4x) = 3(x + -9) * x Reorder the terms: 32 + 4x = 3(-9 + x) * x Reorder the terms for easier multiplication: 32 + 4x = 3x(-9 + x) 32 + 4x = (-9 * 3x + x * 3x) 32 + 4x = (-27x + 3x2) Solving 32 + 4x = -27x + 3x2 Solving for variable 'x'. Combine like terms: 4x + 27x = 31x 32 + 31x + -3x2 = -27x + 3x2 + 27x + -3x2 Reorder the terms: 32 + 31x + -3x2 = -27x + 27x + 3x2 + -3x2 Combine like terms: -27x + 27x = 0 32 + 31x + -3x2 = 0 + 3x2 + -3x2 32 + 31x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 32 + 31x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10.66666667 + -10.33333333x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -10.33333333x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -10.33333333x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -10.33333333x + x2 = 0 + 10.66666667 -10.33333333x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -10.33333333x + x2 = 10.66666667 The x term is -10.33333333x. Take half its coefficient (-5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. -10.33333333x + 26.69444443 + x2 = 10.66666667 + 26.69444443 Reorder the terms: 26.69444443 + -10.33333333x + x2 = 10.66666667 + 26.69444443 Combine like terms: 10.66666667 + 26.69444443 = 37.3611111 26.69444443 + -10.33333333x + x2 = 37.3611111 Factor a perfect square on the left side: (x + -5.166666665)(x + -5.166666665) = 37.3611111 Calculate the square root of the right side: 6.112373606 Break this problem into two subproblems by setting (x + -5.166666665) equal to 6.112373606 and -6.112373606.Subproblem 1
x + -5.166666665 = 6.112373606 Simplifying x + -5.166666665 = 6.112373606 Reorder the terms: -5.166666665 + x = 6.112373606 Solving -5.166666665 + x = 6.112373606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 6.112373606 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 6.112373606 + 5.166666665 x = 6.112373606 + 5.166666665 Combine like terms: 6.112373606 + 5.166666665 = 11.279040271 x = 11.279040271 Simplifying x = 11.279040271Subproblem 2
x + -5.166666665 = -6.112373606 Simplifying x + -5.166666665 = -6.112373606 Reorder the terms: -5.166666665 + x = -6.112373606 Solving -5.166666665 + x = -6.112373606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -6.112373606 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -6.112373606 + 5.166666665 x = -6.112373606 + 5.166666665 Combine like terms: -6.112373606 + 5.166666665 = -0.945706941 x = -0.945706941 Simplifying x = -0.945706941Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.279040271, -0.945706941}
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