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Simplifying -10x(4 + -10x) + 9x = 1 (4 * -10x + -10x * -10x) + 9x = 1 (-40x + 100x2) + 9x = 1 Reorder the terms: -40x + 9x + 100x2 = 1 Combine like terms: -40x + 9x = -31x -31x + 100x2 = 1 Solving -31x + 100x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -31x + 100x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -31x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.01 + -0.31x + x2 = 0.00 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + -0.31x + 0.01 + x2 = 0.00 + 0.01 Reorder the terms: -0.01 + 0.01 + -0.31x + x2 = 0.00 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + -0.31x + x2 = 0.00 + 0.01 -0.31x + x2 = 0.00 + 0.01 Combine like terms: 0.00 + 0.01 = 0.01 -0.31x + x2 = 0.01 The x term is -0.31x. Take half its coefficient (-0.155). Square it (0.024025) and add it to both sides. Add '0.024025' to each side of the equation. -0.31x + 0.024025 + x2 = 0.01 + 0.024025 Reorder the terms: 0.024025 + -0.31x + x2 = 0.01 + 0.024025 Combine like terms: 0.01 + 0.024025 = 0.034025 0.024025 + -0.31x + x2 = 0.034025 Factor a perfect square on the left side: (x + -0.155)(x + -0.155) = 0.034025 Calculate the square root of the right side: 0.184458667 Break this problem into two subproblems by setting (x + -0.155) equal to 0.184458667 and -0.184458667.Subproblem 1
x + -0.155 = 0.184458667 Simplifying x + -0.155 = 0.184458667 Reorder the terms: -0.155 + x = 0.184458667 Solving -0.155 + x = 0.184458667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.155' to each side of the equation. -0.155 + 0.155 + x = 0.184458667 + 0.155 Combine like terms: -0.155 + 0.155 = 0.000 0.000 + x = 0.184458667 + 0.155 x = 0.184458667 + 0.155 Combine like terms: 0.184458667 + 0.155 = 0.339458667 x = 0.339458667 Simplifying x = 0.339458667Subproblem 2
x + -0.155 = -0.184458667 Simplifying x + -0.155 = -0.184458667 Reorder the terms: -0.155 + x = -0.184458667 Solving -0.155 + x = -0.184458667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.155' to each side of the equation. -0.155 + 0.155 + x = -0.184458667 + 0.155 Combine like terms: -0.155 + 0.155 = 0.000 0.000 + x = -0.184458667 + 0.155 x = -0.184458667 + 0.155 Combine like terms: -0.184458667 + 0.155 = -0.029458667 x = -0.029458667 Simplifying x = -0.029458667Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.339458667, -0.029458667}
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