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Simplifying 0 = -16x2 + 212x + -470 Reorder the terms: 0 = -470 + 212x + -16x2 Solving 0 = -470 + 212x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 470 = 470 470 + -212x + 16x2 = -470 + 212x + -16x2 + 470 + -212x + 16x2 Reorder the terms: 470 + -212x + 16x2 = -470 + 470 + 212x + -212x + -16x2 + 16x2 Combine like terms: -470 + 470 = 0 470 + -212x + 16x2 = 0 + 212x + -212x + -16x2 + 16x2 470 + -212x + 16x2 = 212x + -212x + -16x2 + 16x2 Combine like terms: 212x + -212x = 0 470 + -212x + 16x2 = 0 + -16x2 + 16x2 470 + -212x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 470 + -212x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(235 + -106x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(235 + -106x + 8x2)' equal to zero and attempt to solve: Simplifying 235 + -106x + 8x2 = 0 Solving 235 + -106x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 29.375 + -13.25x + x2 = 0 Move the constant term to the right: Add '-29.375' to each side of the equation. 29.375 + -13.25x + -29.375 + x2 = 0 + -29.375 Reorder the terms: 29.375 + -29.375 + -13.25x + x2 = 0 + -29.375 Combine like terms: 29.375 + -29.375 = 0.000 0.000 + -13.25x + x2 = 0 + -29.375 -13.25x + x2 = 0 + -29.375 Combine like terms: 0 + -29.375 = -29.375 -13.25x + x2 = -29.375 The x term is -13.25x. Take half its coefficient (-6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. -13.25x + 43.890625 + x2 = -29.375 + 43.890625 Reorder the terms: 43.890625 + -13.25x + x2 = -29.375 + 43.890625 Combine like terms: -29.375 + 43.890625 = 14.515625 43.890625 + -13.25x + x2 = 14.515625 Factor a perfect square on the left side: (x + -6.625)(x + -6.625) = 14.515625 Calculate the square root of the right side: 3.809937664 Break this problem into two subproblems by setting (x + -6.625) equal to 3.809937664 and -3.809937664.Subproblem 1
x + -6.625 = 3.809937664 Simplifying x + -6.625 = 3.809937664 Reorder the terms: -6.625 + x = 3.809937664 Solving -6.625 + x = 3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = 3.809937664 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = 3.809937664 + 6.625 x = 3.809937664 + 6.625 Combine like terms: 3.809937664 + 6.625 = 10.434937664 x = 10.434937664 Simplifying x = 10.434937664Subproblem 2
x + -6.625 = -3.809937664 Simplifying x + -6.625 = -3.809937664 Reorder the terms: -6.625 + x = -3.809937664 Solving -6.625 + x = -3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = -3.809937664 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = -3.809937664 + 6.625 x = -3.809937664 + 6.625 Combine like terms: -3.809937664 + 6.625 = 2.815062336 x = 2.815062336 Simplifying x = 2.815062336Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.434937664, 2.815062336}Solution
x = {10.434937664, 2.815062336}
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