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Simplifying -10x(4 + -10x + -9) + -7x = 1 Reorder the terms: -10x(4 + -9 + -10x) + -7x = 1 Combine like terms: 4 + -9 = -5 -10x(-5 + -10x) + -7x = 1 (-5 * -10x + -10x * -10x) + -7x = 1 (50x + 100x2) + -7x = 1 Reorder the terms: 50x + -7x + 100x2 = 1 Combine like terms: 50x + -7x = 43x 43x + 100x2 = 1 Solving 43x + 100x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 43x + 100x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 43x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.01 + 0.43x + x2 = 0.00 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + 0.43x + 0.01 + x2 = 0.00 + 0.01 Reorder the terms: -0.01 + 0.01 + 0.43x + x2 = 0.00 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + 0.43x + x2 = 0.00 + 0.01 0.43x + x2 = 0.00 + 0.01 Combine like terms: 0.00 + 0.01 = 0.01 0.43x + x2 = 0.01 The x term is 0.43x. Take half its coefficient (0.215). Square it (0.046225) and add it to both sides. Add '0.046225' to each side of the equation. 0.43x + 0.046225 + x2 = 0.01 + 0.046225 Reorder the terms: 0.046225 + 0.43x + x2 = 0.01 + 0.046225 Combine like terms: 0.01 + 0.046225 = 0.056225 0.046225 + 0.43x + x2 = 0.056225 Factor a perfect square on the left side: (x + 0.215)(x + 0.215) = 0.056225 Calculate the square root of the right side: 0.237118114 Break this problem into two subproblems by setting (x + 0.215) equal to 0.237118114 and -0.237118114.Subproblem 1
x + 0.215 = 0.237118114 Simplifying x + 0.215 = 0.237118114 Reorder the terms: 0.215 + x = 0.237118114 Solving 0.215 + x = 0.237118114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = 0.237118114 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = 0.237118114 + -0.215 x = 0.237118114 + -0.215 Combine like terms: 0.237118114 + -0.215 = 0.022118114 x = 0.022118114 Simplifying x = 0.022118114Subproblem 2
x + 0.215 = -0.237118114 Simplifying x + 0.215 = -0.237118114 Reorder the terms: 0.215 + x = -0.237118114 Solving 0.215 + x = -0.237118114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = -0.237118114 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = -0.237118114 + -0.215 x = -0.237118114 + -0.215 Combine like terms: -0.237118114 + -0.215 = -0.452118114 x = -0.452118114 Simplifying x = -0.452118114Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.022118114, -0.452118114}
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