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Simplifying -16x2 + 14x + 900 = 0 Reorder the terms: 900 + 14x + -16x2 = 0 Solving 900 + 14x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(450 + 7x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(450 + 7x + -8x2)' equal to zero and attempt to solve: Simplifying 450 + 7x + -8x2 = 0 Solving 450 + 7x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -56.25 + -0.875x + x2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -0.875x + 56.25 + x2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -0.875x + x2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -0.875x + x2 = 0 + 56.25 -0.875x + x2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -0.875x + x2 = 56.25 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 = 56.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 56.25 + 0.19140625 Combine like terms: 56.25 + 0.19140625 = 56.44140625 0.19140625 + -0.875x + x2 = 56.44140625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 56.44140625 Calculate the square root of the right side: 7.51274958 Break this problem into two subproblems by setting (x + -0.4375) equal to 7.51274958 and -7.51274958.Subproblem 1
x + -0.4375 = 7.51274958 Simplifying x + -0.4375 = 7.51274958 Reorder the terms: -0.4375 + x = 7.51274958 Solving -0.4375 + x = 7.51274958 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 = 7.51274958 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 7.51274958 + 0.4375 x = 7.51274958 + 0.4375 Combine like terms: 7.51274958 + 0.4375 = 7.95024958 x = 7.95024958 Simplifying x = 7.95024958Subproblem 2
x + -0.4375 = -7.51274958 Simplifying x + -0.4375 = -7.51274958 Reorder the terms: -0.4375 + x = -7.51274958 Solving -0.4375 + x = -7.51274958 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 = -7.51274958 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -7.51274958 + 0.4375 x = -7.51274958 + 0.4375 Combine like terms: -7.51274958 + 0.4375 = -7.07524958 x = -7.07524958 Simplifying x = -7.07524958Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.95024958, -7.07524958}Solution
x = {7.95024958, -7.07524958}
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