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Simplifying -0.01x2 + 0.6x = -5.2 Reorder the terms: 0.6x + -0.01x2 = -5.2 Solving 0.6x + -0.01x2 = -5.2 Solving for variable 'x'. Reorder the terms: 5.2 + 0.6x + -0.01x2 = -5.2 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 5.2 + 0.6x + -0.01x2 = 0.0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -520 + -60x + x2 = 0 Move the constant term to the right: Add '520' to each side of the equation. -520 + -60x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + -60x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + -60x + x2 = 0 + 520 -60x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 -60x + x2 = 520 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 520 + 900 Reorder the terms: 900 + -60x + x2 = 520 + 900 Combine like terms: 520 + 900 = 1420 900 + -60x + x2 = 1420 Factor a perfect square on the left side: (x + -30)(x + -30) = 1420 Calculate the square root of the right side: 37.682887363 Break this problem into two subproblems by setting (x + -30) equal to 37.682887363 and -37.682887363.Subproblem 1
x + -30 = 37.682887363 Simplifying x + -30 = 37.682887363 Reorder the terms: -30 + x = 37.682887363 Solving -30 + x = 37.682887363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 37.682887363 + 30 Combine like terms: -30 + 30 = 0 0 + x = 37.682887363 + 30 x = 37.682887363 + 30 Combine like terms: 37.682887363 + 30 = 67.682887363 x = 67.682887363 Simplifying x = 67.682887363Subproblem 2
x + -30 = -37.682887363 Simplifying x + -30 = -37.682887363 Reorder the terms: -30 + x = -37.682887363 Solving -30 + x = -37.682887363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -37.682887363 + 30 Combine like terms: -30 + 30 = 0 0 + x = -37.682887363 + 30 x = -37.682887363 + 30 Combine like terms: -37.682887363 + 30 = -7.682887363 x = -7.682887363 Simplifying x = -7.682887363Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.682887363, -7.682887363}
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