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Simplifying 16x2 + 2x + -30 = 0 Reorder the terms: -30 + 2x + 16x2 = 0 Solving -30 + 2x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + x + 8x2)' equal to zero and attempt to solve: Simplifying -15 + x + 8x2 = 0 Solving -15 + x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 0.125x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.125x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.125x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.125x + x2 = 0 + 1.875 0.125x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.125x + x2 = 1.875 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125x + 0.25 + x2 = 1.875 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = 1.875 + 0.25 Combine like terms: 1.875 + 0.25 = 2.125 0.25 + 0.125x + x2 = 2.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.125 Calculate the square root of the right side: 1.457737974 Break this problem into two subproblems by setting (x + 0.5) equal to 1.457737974 and -1.457737974.Subproblem 1
x + 0.5 = 1.457737974 Simplifying x + 0.5 = 1.457737974 Reorder the terms: 0.5 + x = 1.457737974 Solving 0.5 + x = 1.457737974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.457737974 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.457737974 + -0.5 x = 1.457737974 + -0.5 Combine like terms: 1.457737974 + -0.5 = 0.957737974 x = 0.957737974 Simplifying x = 0.957737974Subproblem 2
x + 0.5 = -1.457737974 Simplifying x + 0.5 = -1.457737974 Reorder the terms: 0.5 + x = -1.457737974 Solving 0.5 + x = -1.457737974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.457737974 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.457737974 + -0.5 x = -1.457737974 + -0.5 Combine like terms: -1.457737974 + -0.5 = -1.957737974 x = -1.957737974 Simplifying x = -1.957737974Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.957737974, -1.957737974}Solution
x = {0.957737974, -1.957737974}
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