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Simplifying 7 + -1x(x + -4) = 5(1 + -2x) Reorder the terms: 7 + -1x(-4 + x) = 5(1 + -2x) 7 + (-4 * -1x + x * -1x) = 5(1 + -2x) 7 + (4x + -1x2) = 5(1 + -2x) 7 + 4x + -1x2 = (1 * 5 + -2x * 5) 7 + 4x + -1x2 = (5 + -10x) Solving 7 + 4x + -1x2 = 5 + -10x Solving for variable 'x'. Reorder the terms: 7 + -5 + 4x + 10x + -1x2 = 5 + -10x + -5 + 10x Combine like terms: 7 + -5 = 2 2 + 4x + 10x + -1x2 = 5 + -10x + -5 + 10x Combine like terms: 4x + 10x = 14x 2 + 14x + -1x2 = 5 + -10x + -5 + 10x Reorder the terms: 2 + 14x + -1x2 = 5 + -5 + -10x + 10x Combine like terms: 5 + -5 = 0 2 + 14x + -1x2 = 0 + -10x + 10x 2 + 14x + -1x2 = -10x + 10x Combine like terms: -10x + 10x = 0 2 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -14x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -14x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -14x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -14x + x2 = 0 + 2 -14x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -14x + x2 = 2 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 2 + 49 Reorder the terms: 49 + -14x + x2 = 2 + 49 Combine like terms: 2 + 49 = 51 49 + -14x + x2 = 51 Factor a perfect square on the left side: (x + -7)(x + -7) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -7) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -7 = 7.141428429 Simplifying x + -7 = 7.141428429 Reorder the terms: -7 + x = 7.141428429 Solving -7 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.141428429 + 7 x = 7.141428429 + 7 Combine like terms: 7.141428429 + 7 = 14.141428429 x = 14.141428429 Simplifying x = 14.141428429Subproblem 2
x + -7 = -7.141428429 Simplifying x + -7 = -7.141428429 Reorder the terms: -7 + x = -7.141428429 Solving -7 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.141428429 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.141428429 + 7 x = -7.141428429 + 7 Combine like terms: -7.141428429 + 7 = -0.141428429 x = -0.141428429 Simplifying x = -0.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.141428429, -0.141428429}
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