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Simplifying -28x + 12 + -32x2 = 0 Reorder the terms: 12 + -28x + -32x2 = 0 Solving 12 + -28x + -32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -7x + -8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -7x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + -7x + -8x2 = 0 Solving 3 + -7x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 0.875x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.875x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.875x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.875x + x2 = 0 + 0.375 0.875x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.875x + x2 = 0.375 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 = 0.375 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 0.375 + 0.19140625 Combine like terms: 0.375 + 0.19140625 = 0.56640625 0.19140625 + 0.875x + x2 = 0.56640625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
x + 0.4375 = 0.752599661 Simplifying x + 0.4375 = 0.752599661 Reorder the terms: 0.4375 + x = 0.752599661 Solving 0.4375 + x = 0.752599661 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 = 0.752599661 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.752599661 + -0.4375 x = 0.752599661 + -0.4375 Combine like terms: 0.752599661 + -0.4375 = 0.315099661 x = 0.315099661 Simplifying x = 0.315099661Subproblem 2
x + 0.4375 = -0.752599661 Simplifying x + 0.4375 = -0.752599661 Reorder the terms: 0.4375 + x = -0.752599661 Solving 0.4375 + x = -0.752599661 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 = -0.752599661 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.752599661 + -0.4375 x = -0.752599661 + -0.4375 Combine like terms: -0.752599661 + -0.4375 = -1.190099661 x = -1.190099661 Simplifying x = -1.190099661Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.315099661, -1.190099661}Solution
x = {0.315099661, -1.190099661}
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