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Simplifying 16x2 + 64x + -28 = 0 Reorder the terms: -28 + 64x + 16x2 = 0 Solving -28 + 64x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 16x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 16x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 16x + 4x2 = 0 Solving -7 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 4x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 4x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 4x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 4x + x2 = 0 + 1.75 4x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 4x + x2 = 1.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.75 + 4 Reorder the terms: 4 + 4x + x2 = 1.75 + 4 Combine like terms: 1.75 + 4 = 5.75 4 + 4x + x2 = 5.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + 2) equal to 2.397915762 and -2.397915762.Subproblem 1
x + 2 = 2.397915762 Simplifying x + 2 = 2.397915762 Reorder the terms: 2 + x = 2.397915762 Solving 2 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.397915762 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.397915762 + -2 x = 2.397915762 + -2 Combine like terms: 2.397915762 + -2 = 0.397915762 x = 0.397915762 Simplifying x = 0.397915762Subproblem 2
x + 2 = -2.397915762 Simplifying x + 2 = -2.397915762 Reorder the terms: 2 + x = -2.397915762 Solving 2 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.397915762 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.397915762 + -2 x = -2.397915762 + -2 Combine like terms: -2.397915762 + -2 = -4.397915762 x = -4.397915762 Simplifying x = -4.397915762Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.397915762, -4.397915762}Solution
x = {0.397915762, -4.397915762}
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