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Simplifying 4x2 + -90 = 24x Reorder the terms: -90 + 4x2 = 24x Solving -90 + 4x2 = 24x Solving for variable 'x'. Reorder the terms: -90 + -24x + 4x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -90 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying -45 + -12x + 2x2 = 0 Solving -45 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + -6x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -6x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -6x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -6x + x2 = 0 + 22.5 -6x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -6x + x2 = 22.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 22.5 + 9 Reorder the terms: 9 + -6x + x2 = 22.5 + 9 Combine like terms: 22.5 + 9 = 31.5 9 + -6x + x2 = 31.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 31.5 Calculate the square root of the right side: 5.61248608 Break this problem into two subproblems by setting (x + -3) equal to 5.61248608 and -5.61248608.Subproblem 1
x + -3 = 5.61248608 Simplifying x + -3 = 5.61248608 Reorder the terms: -3 + x = 5.61248608 Solving -3 + x = 5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.61248608 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.61248608 + 3 x = 5.61248608 + 3 Combine like terms: 5.61248608 + 3 = 8.61248608 x = 8.61248608 Simplifying x = 8.61248608Subproblem 2
x + -3 = -5.61248608 Simplifying x + -3 = -5.61248608 Reorder the terms: -3 + x = -5.61248608 Solving -3 + x = -5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.61248608 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.61248608 + 3 x = -5.61248608 + 3 Combine like terms: -5.61248608 + 3 = -2.61248608 x = -2.61248608 Simplifying x = -2.61248608Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.61248608, -2.61248608}Solution
x = {8.61248608, -2.61248608}
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