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Simplifying 8x2 + 22x + -10 = 0 Reorder the terms: -10 + 22x + 8x2 = 0 Solving -10 + 22x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 11x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 11x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 11x + 4x2 = 0 Solving -5 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 2.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.75x + x2 = 0 + 1.25 2.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.75x + x2 = 1.25 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 1.25 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 1.25 + 1.890625 Combine like terms: 1.25 + 1.890625 = 3.140625 1.890625 + 2.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 1.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 1.375 = 1.77218086 Simplifying x + 1.375 = 1.77218086 Reorder the terms: 1.375 + x = 1.77218086 Solving 1.375 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 1.77218086 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.77218086 + -1.375 x = 1.77218086 + -1.375 Combine like terms: 1.77218086 + -1.375 = 0.39718086 x = 0.39718086 Simplifying x = 0.39718086Subproblem 2
x + 1.375 = -1.77218086 Simplifying x + 1.375 = -1.77218086 Reorder the terms: 1.375 + x = -1.77218086 Solving 1.375 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -1.77218086 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.77218086 + -1.375 x = -1.77218086 + -1.375 Combine like terms: -1.77218086 + -1.375 = -3.14718086 x = -3.14718086 Simplifying x = -3.14718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.39718086, -3.14718086}Solution
x = {0.39718086, -3.14718086}
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