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Simplifying -24x2 + 21x + 15 = 0 Reorder the terms: 15 + 21x + -24x2 = 0 Solving 15 + 21x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 7x + -8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 7x + -8x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + -8x2 = 0 Solving 5 + 7x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -0.875x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.875x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.875x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.875x + x2 = 0 + 0.625 -0.875x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.875x + x2 = 0.625 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 0.625 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 0.625 + 0.19140625 Combine like terms: 0.625 + 0.19140625 = 0.81640625 0.19140625 + -0.875x + x2 = 0.81640625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (x + -0.4375) equal to 0.903552018 and -0.903552018.Subproblem 1
x + -0.4375 = 0.903552018 Simplifying x + -0.4375 = 0.903552018 Reorder the terms: -0.4375 + x = 0.903552018 Solving -0.4375 + x = 0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.903552018 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.903552018 + 0.4375 x = 0.903552018 + 0.4375 Combine like terms: 0.903552018 + 0.4375 = 1.341052018 x = 1.341052018 Simplifying x = 1.341052018Subproblem 2
x + -0.4375 = -0.903552018 Simplifying x + -0.4375 = -0.903552018 Reorder the terms: -0.4375 + x = -0.903552018 Solving -0.4375 + x = -0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.903552018 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.903552018 + 0.4375 x = -0.903552018 + 0.4375 Combine like terms: -0.903552018 + 0.4375 = -0.466052018 x = -0.466052018 Simplifying x = -0.466052018Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.341052018, -0.466052018}Solution
x = {1.341052018, -0.466052018}
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