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Simplifying 10x2 + -2x = 1575 Reorder the terms: -2x + 10x2 = 1575 Solving -2x + 10x2 = 1575 Solving for variable 'x'. Reorder the terms: -1575 + -2x + 10x2 = 1575 + -1575 Combine like terms: 1575 + -1575 = 0 -1575 + -2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -157.5 + -0.2x + x2 = 0 Move the constant term to the right: Add '157.5' to each side of the equation. -157.5 + -0.2x + 157.5 + x2 = 0 + 157.5 Reorder the terms: -157.5 + 157.5 + -0.2x + x2 = 0 + 157.5 Combine like terms: -157.5 + 157.5 = 0.0 0.0 + -0.2x + x2 = 0 + 157.5 -0.2x + x2 = 0 + 157.5 Combine like terms: 0 + 157.5 = 157.5 -0.2x + x2 = 157.5 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 157.5 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 157.5 + 0.01 Combine like terms: 157.5 + 0.01 = 157.51 0.01 + -0.2x + x2 = 157.51 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 157.51 Calculate the square root of the right side: 12.550298801 Break this problem into two subproblems by setting (x + -0.1) equal to 12.550298801 and -12.550298801.Subproblem 1
x + -0.1 = 12.550298801 Simplifying x + -0.1 = 12.550298801 Reorder the terms: -0.1 + x = 12.550298801 Solving -0.1 + x = 12.550298801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 12.550298801 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 12.550298801 + 0.1 x = 12.550298801 + 0.1 Combine like terms: 12.550298801 + 0.1 = 12.650298801 x = 12.650298801 Simplifying x = 12.650298801Subproblem 2
x + -0.1 = -12.550298801 Simplifying x + -0.1 = -12.550298801 Reorder the terms: -0.1 + x = -12.550298801 Solving -0.1 + x = -12.550298801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -12.550298801 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -12.550298801 + 0.1 x = -12.550298801 + 0.1 Combine like terms: -12.550298801 + 0.1 = -12.450298801 x = -12.450298801 Simplifying x = -12.450298801Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.650298801, -12.450298801}
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