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Simplifying -16x2 + 34.3x + 8 = 0 Reorder the terms: 8 + 34.3x + -16x2 = 0 Solving 8 + 34.3x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5 + -2.14375x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.14375x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.14375x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.14375x + x2 = 0 + 0.5 -2.14375x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.14375x + x2 = 0.5 The x term is -2.14375x. Take half its coefficient (-1.071875). Square it (1.148916016) and add it to both sides. Add '1.148916016' to each side of the equation. -2.14375x + 1.148916016 + x2 = 0.5 + 1.148916016 Reorder the terms: 1.148916016 + -2.14375x + x2 = 0.5 + 1.148916016 Combine like terms: 0.5 + 1.148916016 = 1.648916016 1.148916016 + -2.14375x + x2 = 1.648916016 Factor a perfect square on the left side: (x + -1.071875)(x + -1.071875) = 1.648916016 Calculate the square root of the right side: 1.284101248 Break this problem into two subproblems by setting (x + -1.071875) equal to 1.284101248 and -1.284101248.Subproblem 1
x + -1.071875 = 1.284101248 Simplifying x + -1.071875 = 1.284101248 Reorder the terms: -1.071875 + x = 1.284101248 Solving -1.071875 + x = 1.284101248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071875' to each side of the equation. -1.071875 + 1.071875 + x = 1.284101248 + 1.071875 Combine like terms: -1.071875 + 1.071875 = 0.000000 0.000000 + x = 1.284101248 + 1.071875 x = 1.284101248 + 1.071875 Combine like terms: 1.284101248 + 1.071875 = 2.355976248 x = 2.355976248 Simplifying x = 2.355976248Subproblem 2
x + -1.071875 = -1.284101248 Simplifying x + -1.071875 = -1.284101248 Reorder the terms: -1.071875 + x = -1.284101248 Solving -1.071875 + x = -1.284101248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071875' to each side of the equation. -1.071875 + 1.071875 + x = -1.284101248 + 1.071875 Combine like terms: -1.071875 + 1.071875 = 0.000000 0.000000 + x = -1.284101248 + 1.071875 x = -1.284101248 + 1.071875 Combine like terms: -1.284101248 + 1.071875 = -0.212226248 x = -0.212226248 Simplifying x = -0.212226248Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.355976248, -0.212226248}
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