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Simplifying 10x(x + -2) = 5 + -1(x + 4) Reorder the terms: 10x(-2 + x) = 5 + -1(x + 4) (-2 * 10x + x * 10x) = 5 + -1(x + 4) (-20x + 10x2) = 5 + -1(x + 4) Reorder the terms: -20x + 10x2 = 5 + -1(4 + x) -20x + 10x2 = 5 + (4 * -1 + x * -1) -20x + 10x2 = 5 + (-4 + -1x) Combine like terms: 5 + -4 = 1 -20x + 10x2 = 1 + -1x Solving -20x + 10x2 = 1 + -1x Solving for variable 'x'. Reorder the terms: -1 + -20x + x + 10x2 = 1 + -1x + -1 + x Combine like terms: -20x + x = -19x -1 + -19x + 10x2 = 1 + -1x + -1 + x Reorder the terms: -1 + -19x + 10x2 = 1 + -1 + -1x + x Combine like terms: 1 + -1 = 0 -1 + -19x + 10x2 = 0 + -1x + x -1 + -19x + 10x2 = -1x + x Combine like terms: -1x + x = 0 -1 + -19x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + -1.9x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -1.9x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -1.9x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -1.9x + x2 = 0 + 0.1 -1.9x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -1.9x + x2 = 0.1 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = 0.1 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = 0.1 + 0.9025 Combine like terms: 0.1 + 0.9025 = 1.0025 0.9025 + -1.9x + x2 = 1.0025 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 1.0025 Calculate the square root of the right side: 1.00124922 Break this problem into two subproblems by setting (x + -0.95) equal to 1.00124922 and -1.00124922.Subproblem 1
x + -0.95 = 1.00124922 Simplifying x + -0.95 = 1.00124922 Reorder the terms: -0.95 + x = 1.00124922 Solving -0.95 + x = 1.00124922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 1.00124922 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 1.00124922 + 0.95 x = 1.00124922 + 0.95 Combine like terms: 1.00124922 + 0.95 = 1.95124922 x = 1.95124922 Simplifying x = 1.95124922Subproblem 2
x + -0.95 = -1.00124922 Simplifying x + -0.95 = -1.00124922 Reorder the terms: -0.95 + x = -1.00124922 Solving -0.95 + x = -1.00124922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -1.00124922 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -1.00124922 + 0.95 x = -1.00124922 + 0.95 Combine like terms: -1.00124922 + 0.95 = -0.05124922 x = -0.05124922 Simplifying x = -0.05124922Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.95124922, -0.05124922}
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