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Simplifying 40 = -3x2 + 12x + 135 Reorder the terms: 40 = 135 + 12x + -3x2 Solving 40 = 135 + 12x + -3x2 Solving for variable 'x'. Combine like terms: 40 + -135 = -95 -95 + -12x + 3x2 = 135 + 12x + -3x2 + -135 + -12x + 3x2 Reorder the terms: -95 + -12x + 3x2 = 135 + -135 + 12x + -12x + -3x2 + 3x2 Combine like terms: 135 + -135 = 0 -95 + -12x + 3x2 = 0 + 12x + -12x + -3x2 + 3x2 -95 + -12x + 3x2 = 12x + -12x + -3x2 + 3x2 Combine like terms: 12x + -12x = 0 -95 + -12x + 3x2 = 0 + -3x2 + 3x2 -95 + -12x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -95 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -31.66666667 + -4x + x2 = 0 Move the constant term to the right: Add '31.66666667' to each side of the equation. -31.66666667 + -4x + 31.66666667 + x2 = 0 + 31.66666667 Reorder the terms: -31.66666667 + 31.66666667 + -4x + x2 = 0 + 31.66666667 Combine like terms: -31.66666667 + 31.66666667 = 0.00000000 0.00000000 + -4x + x2 = 0 + 31.66666667 -4x + x2 = 0 + 31.66666667 Combine like terms: 0 + 31.66666667 = 31.66666667 -4x + x2 = 31.66666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 31.66666667 + 4 Reorder the terms: 4 + -4x + x2 = 31.66666667 + 4 Combine like terms: 31.66666667 + 4 = 35.66666667 4 + -4x + x2 = 35.66666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 35.66666667 Calculate the square root of the right side: 5.972157623 Break this problem into two subproblems by setting (x + -2) equal to 5.972157623 and -5.972157623.Subproblem 1
x + -2 = 5.972157623 Simplifying x + -2 = 5.972157623 Reorder the terms: -2 + x = 5.972157623 Solving -2 + x = 5.972157623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.972157623 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.972157623 + 2 x = 5.972157623 + 2 Combine like terms: 5.972157623 + 2 = 7.972157623 x = 7.972157623 Simplifying x = 7.972157623Subproblem 2
x + -2 = -5.972157623 Simplifying x + -2 = -5.972157623 Reorder the terms: -2 + x = -5.972157623 Solving -2 + x = -5.972157623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.972157623 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.972157623 + 2 x = -5.972157623 + 2 Combine like terms: -5.972157623 + 2 = -3.972157623 x = -3.972157623 Simplifying x = -3.972157623Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.972157623, -3.972157623}
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