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Simplifying 144x2 + -120x + 25 = 110 Reorder the terms: 25 + -120x + 144x2 = 110 Solving 25 + -120x + 144x2 = 110 Solving for variable 'x'. Reorder the terms: 25 + -110 + -120x + 144x2 = 110 + -110 Combine like terms: 25 + -110 = -85 -85 + -120x + 144x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -85 + -120x + 144x2 = 0 Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.5902777778 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.5902777778' to each side of the equation. -0.5902777778 + -0.8333333333x + 0.5902777778 + x2 = 0 + 0.5902777778 Reorder the terms: -0.5902777778 + 0.5902777778 + -0.8333333333x + x2 = 0 + 0.5902777778 Combine like terms: -0.5902777778 + 0.5902777778 = 0.0000000000 0.0000000000 + -0.8333333333x + x2 = 0 + 0.5902777778 -0.8333333333x + x2 = 0 + 0.5902777778 Combine like terms: 0 + 0.5902777778 = 0.5902777778 -0.8333333333x + x2 = 0.5902777778 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 0.5902777778 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 0.5902777778 + 0.1736111111 Combine like terms: 0.5902777778 + 0.1736111111 = 0.7638888889 0.1736111111 + -0.8333333333x + x2 = 0.7638888889 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 0.7638888889 Calculate the square root of the right side: 0.874007373 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 0.874007373 and -0.874007373.Subproblem 1
x + -0.4166666667 = 0.874007373 Simplifying x + -0.4166666667 = 0.874007373 Reorder the terms: -0.4166666667 + x = 0.874007373 Solving -0.4166666667 + x = 0.874007373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 0.874007373 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.874007373 + 0.4166666667 x = 0.874007373 + 0.4166666667 Combine like terms: 0.874007373 + 0.4166666667 = 1.2906740397 x = 1.2906740397 Simplifying x = 1.2906740397Subproblem 2
x + -0.4166666667 = -0.874007373 Simplifying x + -0.4166666667 = -0.874007373 Reorder the terms: -0.4166666667 + x = -0.874007373 Solving -0.4166666667 + x = -0.874007373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -0.874007373 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.874007373 + 0.4166666667 x = -0.874007373 + 0.4166666667 Combine like terms: -0.874007373 + 0.4166666667 = -0.4573407063 x = -0.4573407063 Simplifying x = -0.4573407063Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2906740397, -0.4573407063}
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