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Simplifying 90 = 15x2 + -2x + -24 Reorder the terms: 90 = -24 + -2x + 15x2 Solving 90 = -24 + -2x + 15x2 Solving for variable 'x'. Combine like terms: 90 + 24 = 114 114 + 2x + -15x2 = -24 + -2x + 15x2 + 24 + 2x + -15x2 Reorder the terms: 114 + 2x + -15x2 = -24 + 24 + -2x + 2x + 15x2 + -15x2 Combine like terms: -24 + 24 = 0 114 + 2x + -15x2 = 0 + -2x + 2x + 15x2 + -15x2 114 + 2x + -15x2 = -2x + 2x + 15x2 + -15x2 Combine like terms: -2x + 2x = 0 114 + 2x + -15x2 = 0 + 15x2 + -15x2 114 + 2x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 114 + 2x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -7.6 + -0.1333333333x + x2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -0.1333333333x + 7.6 + x2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -0.1333333333x + x2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -0.1333333333x + x2 = 0 + 7.6 -0.1333333333x + x2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -0.1333333333x + x2 = 7.6 The x term is -0.1333333333x. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333x + 0.004444444442 + x2 = 7.6 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333x + x2 = 7.6 + 0.004444444442 Combine like terms: 7.6 + 0.004444444442 = 7.604444444442 0.004444444442 + -0.1333333333x + x2 = 7.604444444442 Factor a perfect square on the left side: (x + -0.06666666665)(x + -0.06666666665) = 7.604444444442 Calculate the square root of the right side: 2.757615717 Break this problem into two subproblems by setting (x + -0.06666666665) equal to 2.757615717 and -2.757615717.Subproblem 1
x + -0.06666666665 = 2.757615717 Simplifying x + -0.06666666665 = 2.757615717 Reorder the terms: -0.06666666665 + x = 2.757615717 Solving -0.06666666665 + x = 2.757615717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = 2.757615717 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = 2.757615717 + 0.06666666665 x = 2.757615717 + 0.06666666665 Combine like terms: 2.757615717 + 0.06666666665 = 2.82428238365 x = 2.82428238365 Simplifying x = 2.82428238365Subproblem 2
x + -0.06666666665 = -2.757615717 Simplifying x + -0.06666666665 = -2.757615717 Reorder the terms: -0.06666666665 + x = -2.757615717 Solving -0.06666666665 + x = -2.757615717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = -2.757615717 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = -2.757615717 + 0.06666666665 x = -2.757615717 + 0.06666666665 Combine like terms: -2.757615717 + 0.06666666665 = -2.69094905035 x = -2.69094905035 Simplifying x = -2.69094905035Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.82428238365, -2.69094905035}
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