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Simplifying 16x2 + 32x + -284 = 0 Reorder the terms: -284 + 32x + 16x2 = 0 Solving -284 + 32x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-71 + 8x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-71 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying -71 + 8x + 4x2 = 0 Solving -71 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.75 + 2x + x2 = 0 Move the constant term to the right: Add '17.75' to each side of the equation. -17.75 + 2x + 17.75 + x2 = 0 + 17.75 Reorder the terms: -17.75 + 17.75 + 2x + x2 = 0 + 17.75 Combine like terms: -17.75 + 17.75 = 0.00 0.00 + 2x + x2 = 0 + 17.75 2x + x2 = 0 + 17.75 Combine like terms: 0 + 17.75 = 17.75 2x + x2 = 17.75 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 17.75 + 1 Reorder the terms: 1 + 2x + x2 = 17.75 + 1 Combine like terms: 17.75 + 1 = 18.75 1 + 2x + x2 = 18.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + 1) equal to 4.330127019 and -4.330127019.Subproblem 1
x + 1 = 4.330127019 Simplifying x + 1 = 4.330127019 Reorder the terms: 1 + x = 4.330127019 Solving 1 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.330127019 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.330127019 + -1 x = 4.330127019 + -1 Combine like terms: 4.330127019 + -1 = 3.330127019 x = 3.330127019 Simplifying x = 3.330127019Subproblem 2
x + 1 = -4.330127019 Simplifying x + 1 = -4.330127019 Reorder the terms: 1 + x = -4.330127019 Solving 1 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.330127019 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.330127019 + -1 x = -4.330127019 + -1 Combine like terms: -4.330127019 + -1 = -5.330127019 x = -5.330127019 Simplifying x = -5.330127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.330127019, -5.330127019}Solution
x = {3.330127019, -5.330127019}
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