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Simplifying 4x(2x + -6) = 90 Reorder the terms: 4x(-6 + 2x) = 90 (-6 * 4x + 2x * 4x) = 90 (-24x + 8x2) = 90 Solving -24x + 8x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -24x + 8x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -24x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -12x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -12x + 4x2)' equal to zero and attempt to solve: Simplifying -45 + -12x + 4x2 = 0 Solving -45 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -3x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -3x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -3x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -3x + x2 = 0 + 11.25 -3x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -3x + x2 = 11.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 11.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 11.25 + 2.25 Combine like terms: 11.25 + 2.25 = 13.5 2.25 + -3x + x2 = 13.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + -1.5) equal to 3.674234614 and -3.674234614.Subproblem 1
x + -1.5 = 3.674234614 Simplifying x + -1.5 = 3.674234614 Reorder the terms: -1.5 + x = 3.674234614 Solving -1.5 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.674234614 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.674234614 + 1.5 x = 3.674234614 + 1.5 Combine like terms: 3.674234614 + 1.5 = 5.174234614 x = 5.174234614 Simplifying x = 5.174234614Subproblem 2
x + -1.5 = -3.674234614 Simplifying x + -1.5 = -3.674234614 Reorder the terms: -1.5 + x = -3.674234614 Solving -1.5 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.674234614 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.674234614 + 1.5 x = -3.674234614 + 1.5 Combine like terms: -3.674234614 + 1.5 = -2.174234614 x = -2.174234614 Simplifying x = -2.174234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.174234614, -2.174234614}Solution
x = {5.174234614, -2.174234614}
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