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Simplifying 0 = 4x2 + -47x + -70 Reorder the terms: 0 = -70 + -47x + 4x2 Solving 0 = -70 + -47x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 70 = 70 70 + 47x + -4x2 = -70 + -47x + 4x2 + 70 + 47x + -4x2 Reorder the terms: 70 + 47x + -4x2 = -70 + 70 + -47x + 47x + 4x2 + -4x2 Combine like terms: -70 + 70 = 0 70 + 47x + -4x2 = 0 + -47x + 47x + 4x2 + -4x2 70 + 47x + -4x2 = -47x + 47x + 4x2 + -4x2 Combine like terms: -47x + 47x = 0 70 + 47x + -4x2 = 0 + 4x2 + -4x2 70 + 47x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 70 + 47x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -17.5 + -11.75x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -11.75x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -11.75x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -11.75x + x2 = 0 + 17.5 -11.75x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -11.75x + x2 = 17.5 The x term is -11.75x. Take half its coefficient (-5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. -11.75x + 34.515625 + x2 = 17.5 + 34.515625 Reorder the terms: 34.515625 + -11.75x + x2 = 17.5 + 34.515625 Combine like terms: 17.5 + 34.515625 = 52.015625 34.515625 + -11.75x + x2 = 52.015625 Factor a perfect square on the left side: (x + -5.875)(x + -5.875) = 52.015625 Calculate the square root of the right side: 7.212185868 Break this problem into two subproblems by setting (x + -5.875) equal to 7.212185868 and -7.212185868.Subproblem 1
x + -5.875 = 7.212185868 Simplifying x + -5.875 = 7.212185868 Reorder the terms: -5.875 + x = 7.212185868 Solving -5.875 + x = 7.212185868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.875' to each side of the equation. -5.875 + 5.875 + x = 7.212185868 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + x = 7.212185868 + 5.875 x = 7.212185868 + 5.875 Combine like terms: 7.212185868 + 5.875 = 13.087185868 x = 13.087185868 Simplifying x = 13.087185868Subproblem 2
x + -5.875 = -7.212185868 Simplifying x + -5.875 = -7.212185868 Reorder the terms: -5.875 + x = -7.212185868 Solving -5.875 + x = -7.212185868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.875' to each side of the equation. -5.875 + 5.875 + x = -7.212185868 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + x = -7.212185868 + 5.875 x = -7.212185868 + 5.875 Combine like terms: -7.212185868 + 5.875 = -1.337185868 x = -1.337185868 Simplifying x = -1.337185868Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.087185868, -1.337185868}
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