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Simplifying 56x2 + -104.75x + 44.625 = 0 Reorder the terms: 44.625 + -104.75x + 56x2 = 0 Solving 44.625 + -104.75x + 56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 0.796875 + -1.870535714x + x2 = 0 Move the constant term to the right: Add '-0.796875' to each side of the equation. 0.796875 + -1.870535714x + -0.796875 + x2 = 0 + -0.796875 Reorder the terms: 0.796875 + -0.796875 + -1.870535714x + x2 = 0 + -0.796875 Combine like terms: 0.796875 + -0.796875 = 0.000000 0.000000 + -1.870535714x + x2 = 0 + -0.796875 -1.870535714x + x2 = 0 + -0.796875 Combine like terms: 0 + -0.796875 = -0.796875 -1.870535714x + x2 = -0.796875 The x term is -1.870535714x. Take half its coefficient (-0.935267857). Square it (0.8747259643) and add it to both sides. Add '0.8747259643' to each side of the equation. -1.870535714x + 0.8747259643 + x2 = -0.796875 + 0.8747259643 Reorder the terms: 0.8747259643 + -1.870535714x + x2 = -0.796875 + 0.8747259643 Combine like terms: -0.796875 + 0.8747259643 = 0.0778509643 0.8747259643 + -1.870535714x + x2 = 0.0778509643 Factor a perfect square on the left side: (x + -0.935267857)(x + -0.935267857) = 0.0778509643 Calculate the square root of the right side: 0.279017857 Break this problem into two subproblems by setting (x + -0.935267857) equal to 0.279017857 and -0.279017857.Subproblem 1
x + -0.935267857 = 0.279017857 Simplifying x + -0.935267857 = 0.279017857 Reorder the terms: -0.935267857 + x = 0.279017857 Solving -0.935267857 + x = 0.279017857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.935267857' to each side of the equation. -0.935267857 + 0.935267857 + x = 0.279017857 + 0.935267857 Combine like terms: -0.935267857 + 0.935267857 = 0.000000000 0.000000000 + x = 0.279017857 + 0.935267857 x = 0.279017857 + 0.935267857 Combine like terms: 0.279017857 + 0.935267857 = 1.214285714 x = 1.214285714 Simplifying x = 1.214285714Subproblem 2
x + -0.935267857 = -0.279017857 Simplifying x + -0.935267857 = -0.279017857 Reorder the terms: -0.935267857 + x = -0.279017857 Solving -0.935267857 + x = -0.279017857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.935267857' to each side of the equation. -0.935267857 + 0.935267857 + x = -0.279017857 + 0.935267857 Combine like terms: -0.935267857 + 0.935267857 = 0.000000000 0.000000000 + x = -0.279017857 + 0.935267857 x = -0.279017857 + 0.935267857 Combine like terms: -0.279017857 + 0.935267857 = 0.65625 x = 0.65625 Simplifying x = 0.65625Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.214285714, 0.65625}
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