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Simplifying 10x2 + -69x + 118 = 0 Reorder the terms: 118 + -69x + 10x2 = 0 Solving 118 + -69x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 11.8 + -6.9x + x2 = 0 Move the constant term to the right: Add '-11.8' to each side of the equation. 11.8 + -6.9x + -11.8 + x2 = 0 + -11.8 Reorder the terms: 11.8 + -11.8 + -6.9x + x2 = 0 + -11.8 Combine like terms: 11.8 + -11.8 = 0.0 0.0 + -6.9x + x2 = 0 + -11.8 -6.9x + x2 = 0 + -11.8 Combine like terms: 0 + -11.8 = -11.8 -6.9x + x2 = -11.8 The x term is -6.9x. Take half its coefficient (-3.45). Square it (11.9025) and add it to both sides. Add '11.9025' to each side of the equation. -6.9x + 11.9025 + x2 = -11.8 + 11.9025 Reorder the terms: 11.9025 + -6.9x + x2 = -11.8 + 11.9025 Combine like terms: -11.8 + 11.9025 = 0.1025 11.9025 + -6.9x + x2 = 0.1025 Factor a perfect square on the left side: (x + -3.45)(x + -3.45) = 0.1025 Calculate the square root of the right side: 0.320156212 Break this problem into two subproblems by setting (x + -3.45) equal to 0.320156212 and -0.320156212.Subproblem 1
x + -3.45 = 0.320156212 Simplifying x + -3.45 = 0.320156212 Reorder the terms: -3.45 + x = 0.320156212 Solving -3.45 + x = 0.320156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.45' to each side of the equation. -3.45 + 3.45 + x = 0.320156212 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + x = 0.320156212 + 3.45 x = 0.320156212 + 3.45 Combine like terms: 0.320156212 + 3.45 = 3.770156212 x = 3.770156212 Simplifying x = 3.770156212Subproblem 2
x + -3.45 = -0.320156212 Simplifying x + -3.45 = -0.320156212 Reorder the terms: -3.45 + x = -0.320156212 Solving -3.45 + x = -0.320156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.45' to each side of the equation. -3.45 + 3.45 + x = -0.320156212 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + x = -0.320156212 + 3.45 x = -0.320156212 + 3.45 Combine like terms: -0.320156212 + 3.45 = 3.129843788 x = 3.129843788 Simplifying x = 3.129843788Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.770156212, 3.129843788}
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