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Simplifying 10x2 + -9x + -1368 = 0 Reorder the terms: -1368 + -9x + 10x2 = 0 Solving -1368 + -9x + 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'. -136.8 + -0.9x + x2 = 0 Move the constant term to the right: Add '136.8' to each side of the equation. -136.8 + -0.9x + 136.8 + x2 = 0 + 136.8 Reorder the terms: -136.8 + 136.8 + -0.9x + x2 = 0 + 136.8 Combine like terms: -136.8 + 136.8 = 0.0 0.0 + -0.9x + x2 = 0 + 136.8 -0.9x + x2 = 0 + 136.8 Combine like terms: 0 + 136.8 = 136.8 -0.9x + x2 = 136.8 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = 136.8 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 136.8 + 0.2025 Combine like terms: 136.8 + 0.2025 = 137.0025 0.2025 + -0.9x + x2 = 137.0025 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 137.0025 Calculate the square root of the right side: 11.704806705 Break this problem into two subproblems by setting (x + -0.45) equal to 11.704806705 and -11.704806705.Subproblem 1
x + -0.45 = 11.704806705 Simplifying x + -0.45 = 11.704806705 Reorder the terms: -0.45 + x = 11.704806705 Solving -0.45 + x = 11.704806705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 11.704806705 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 11.704806705 + 0.45 x = 11.704806705 + 0.45 Combine like terms: 11.704806705 + 0.45 = 12.154806705 x = 12.154806705 Simplifying x = 12.154806705Subproblem 2
x + -0.45 = -11.704806705 Simplifying x + -0.45 = -11.704806705 Reorder the terms: -0.45 + x = -11.704806705 Solving -0.45 + x = -11.704806705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -11.704806705 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -11.704806705 + 0.45 x = -11.704806705 + 0.45 Combine like terms: -11.704806705 + 0.45 = -11.254806705 x = -11.254806705 Simplifying x = -11.254806705Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.154806705, -11.254806705}
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