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Simplifying -16x2 + 90x + 2 = 0 Reorder the terms: 2 + 90x + -16x2 = 0 Solving 2 + 90x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 45x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 45x + -8x2)' equal to zero and attempt to solve: Simplifying 1 + 45x + -8x2 = 0 Solving 1 + 45x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -5.625x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -5.625x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -5.625x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -5.625x + x2 = 0 + 0.125 -5.625x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -5.625x + x2 = 0.125 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = 0.125 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = 0.125 + 7.91015625 Combine like terms: 0.125 + 7.91015625 = 8.03515625 7.91015625 + -5.625x + x2 = 8.03515625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 8.03515625 Calculate the square root of the right side: 2.834635118 Break this problem into two subproblems by setting (x + -2.8125) equal to 2.834635118 and -2.834635118.Subproblem 1
x + -2.8125 = 2.834635118 Simplifying x + -2.8125 = 2.834635118 Reorder the terms: -2.8125 + x = 2.834635118 Solving -2.8125 + x = 2.834635118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 2.834635118 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 2.834635118 + 2.8125 x = 2.834635118 + 2.8125 Combine like terms: 2.834635118 + 2.8125 = 5.647135118 x = 5.647135118 Simplifying x = 5.647135118Subproblem 2
x + -2.8125 = -2.834635118 Simplifying x + -2.8125 = -2.834635118 Reorder the terms: -2.8125 + x = -2.834635118 Solving -2.8125 + x = -2.834635118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -2.834635118 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -2.834635118 + 2.8125 x = -2.834635118 + 2.8125 Combine like terms: -2.834635118 + 2.8125 = -0.022135118 x = -0.022135118 Simplifying x = -0.022135118Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.647135118, -0.022135118}Solution
x = {5.647135118, -0.022135118}
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