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Simplifying 16x2 + 4x + -70 = 0 Reorder the terms: -70 + 4x + 16x2 = 0 Solving -70 + 4x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 2x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 2x + 8x2)' equal to zero and attempt to solve: Simplifying -35 + 2x + 8x2 = 0 Solving -35 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + 0.25x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 0.25x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 0.25x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 0.25x + x2 = 0 + 4.375 0.25x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 0.25x + x2 = 4.375 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 4.375 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 4.375 + 0.015625 Combine like terms: 4.375 + 0.015625 = 4.390625 0.015625 + 0.25x + x2 = 4.390625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + 0.125) equal to 2.095381827 and -2.095381827.Subproblem 1
x + 0.125 = 2.095381827 Simplifying x + 0.125 = 2.095381827 Reorder the terms: 0.125 + x = 2.095381827 Solving 0.125 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 2.095381827 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 2.095381827 + -0.125 x = 2.095381827 + -0.125 Combine like terms: 2.095381827 + -0.125 = 1.970381827 x = 1.970381827 Simplifying x = 1.970381827Subproblem 2
x + 0.125 = -2.095381827 Simplifying x + 0.125 = -2.095381827 Reorder the terms: 0.125 + x = -2.095381827 Solving 0.125 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -2.095381827 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -2.095381827 + -0.125 x = -2.095381827 + -0.125 Combine like terms: -2.095381827 + -0.125 = -2.220381827 x = -2.220381827 Simplifying x = -2.220381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.970381827, -2.220381827}Solution
x = {1.970381827, -2.220381827}
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