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Simplifying -15 = 6x * x + 25x Multiply x * x -15 = 6x2 + 25x Reorder the terms: -15 = 25x + 6x2 Solving -15 = 25x + 6x2 Solving for variable 'x'. Reorder the terms: -15 + -25x + -6x2 = 25x + -25x + 6x2 + -6x2 Combine like terms: 25x + -25x = 0 -15 + -25x + -6x2 = 0 + 6x2 + -6x2 -15 + -25x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -15 + -25x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 25x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 25x + 6x2)' equal to zero and attempt to solve: Simplifying 15 + 25x + 6x2 = 0 Solving 15 + 25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 4.166666667x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 4.166666667x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 4.166666667x + x2 = 0 + -2.5 4.166666667x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 4.166666667x + x2 = -2.5 The x term is 4.166666667x. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667x + 4.340277781 + x2 = -2.5 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = -2.5 + 4.340277781 Combine like terms: -2.5 + 4.340277781 = 1.840277781 4.340277781 + 4.166666667x + x2 = 1.840277781 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 1.840277781 Calculate the square root of the right side: 1.356568384 Break this problem into two subproblems by setting (x + 2.083333334) equal to 1.356568384 and -1.356568384.Subproblem 1
x + 2.083333334 = 1.356568384 Simplifying x + 2.083333334 = 1.356568384 Reorder the terms: 2.083333334 + x = 1.356568384 Solving 2.083333334 + x = 1.356568384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = 1.356568384 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 1.356568384 + -2.083333334 x = 1.356568384 + -2.083333334 Combine like terms: 1.356568384 + -2.083333334 = -0.72676495 x = -0.72676495 Simplifying x = -0.72676495Subproblem 2
x + 2.083333334 = -1.356568384 Simplifying x + 2.083333334 = -1.356568384 Reorder the terms: 2.083333334 + x = -1.356568384 Solving 2.083333334 + x = -1.356568384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = -1.356568384 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -1.356568384 + -2.083333334 x = -1.356568384 + -2.083333334 Combine like terms: -1.356568384 + -2.083333334 = -3.439901718 x = -3.439901718 Simplifying x = -3.439901718Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.72676495, -3.439901718}Solution
x = {-0.72676495, -3.439901718}
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