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Simplifying -3x2 + 24x + -15 = 0 Reorder the terms: -15 + 24x + -3x2 = 0 Solving -15 + 24x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 8x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 8x + -1x2 = 0 Solving -5 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -8x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -8x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x + x2 = 0 + -5 -8x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8x + x2 = -5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -5 + 16 Reorder the terms: 16 + -8x + x2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8x + x2 = 11 Factor a perfect square on the left side: (x + -4)(x + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -4 = 3.31662479 Simplifying x + -4 = 3.31662479 Reorder the terms: -4 + x = 3.31662479 Solving -4 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.31662479 + 4 x = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x = 7.31662479 Simplifying x = 7.31662479Subproblem 2
x + -4 = -3.31662479 Simplifying x + -4 = -3.31662479 Reorder the terms: -4 + x = -3.31662479 Solving -4 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.31662479 + 4 x = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x = 0.68337521 Simplifying x = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.31662479, 0.68337521}Solution
x = {7.31662479, 0.68337521}
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