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Simplifying 10x2 + -69x + 10 = 0 Reorder the terms: 10 + -69x + 10x2 = 0 Solving 10 + -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'. 1 + -6.9x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6.9x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -6.9x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6.9x + x2 = 0 + -1 -6.9x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6.9x + x2 = -1 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 = -1 + 11.9025 Reorder the terms: 11.9025 + -6.9x + x2 = -1 + 11.9025 Combine like terms: -1 + 11.9025 = 10.9025 11.9025 + -6.9x + x2 = 10.9025 Factor a perfect square on the left side: (x + -3.45)(x + -3.45) = 10.9025 Calculate the square root of the right side: 3.301893396 Break this problem into two subproblems by setting (x + -3.45) equal to 3.301893396 and -3.301893396.Subproblem 1
x + -3.45 = 3.301893396 Simplifying x + -3.45 = 3.301893396 Reorder the terms: -3.45 + x = 3.301893396 Solving -3.45 + x = 3.301893396 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 = 3.301893396 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + x = 3.301893396 + 3.45 x = 3.301893396 + 3.45 Combine like terms: 3.301893396 + 3.45 = 6.751893396 x = 6.751893396 Simplifying x = 6.751893396Subproblem 2
x + -3.45 = -3.301893396 Simplifying x + -3.45 = -3.301893396 Reorder the terms: -3.45 + x = -3.301893396 Solving -3.45 + x = -3.301893396 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 = -3.301893396 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + x = -3.301893396 + 3.45 x = -3.301893396 + 3.45 Combine like terms: -3.301893396 + 3.45 = 0.148106604 x = 0.148106604 Simplifying x = 0.148106604Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.751893396, 0.148106604}
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