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Simplifying (5x + -4)(x + 10) = 7 Reorder the terms: (-4 + 5x)(x + 10) = 7 Reorder the terms: (-4 + 5x)(10 + x) = 7 Multiply (-4 + 5x) * (10 + x) (-4(10 + x) + 5x * (10 + x)) = 7 ((10 * -4 + x * -4) + 5x * (10 + x)) = 7 ((-40 + -4x) + 5x * (10 + x)) = 7 (-40 + -4x + (10 * 5x + x * 5x)) = 7 (-40 + -4x + (50x + 5x2)) = 7 Combine like terms: -4x + 50x = 46x (-40 + 46x + 5x2) = 7 Solving -40 + 46x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -40 + -7 + 46x + 5x2 = 7 + -7 Combine like terms: -40 + -7 = -47 -47 + 46x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -47 + 46x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.4 + 9.2x + x2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + 9.2x + 9.4 + x2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + 9.2x + x2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + 9.2x + x2 = 0 + 9.4 9.2x + x2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 9.2x + x2 = 9.4 The x term is 9.2x. Take half its coefficient (4.6). Square it (21.16) and add it to both sides. Add '21.16' to each side of the equation. 9.2x + 21.16 + x2 = 9.4 + 21.16 Reorder the terms: 21.16 + 9.2x + x2 = 9.4 + 21.16 Combine like terms: 9.4 + 21.16 = 30.56 21.16 + 9.2x + x2 = 30.56 Factor a perfect square on the left side: (x + 4.6)(x + 4.6) = 30.56 Calculate the square root of the right side: 5.528109984 Break this problem into two subproblems by setting (x + 4.6) equal to 5.528109984 and -5.528109984.Subproblem 1
x + 4.6 = 5.528109984 Simplifying x + 4.6 = 5.528109984 Reorder the terms: 4.6 + x = 5.528109984 Solving 4.6 + x = 5.528109984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6' to each side of the equation. 4.6 + -4.6 + x = 5.528109984 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + x = 5.528109984 + -4.6 x = 5.528109984 + -4.6 Combine like terms: 5.528109984 + -4.6 = 0.928109984 x = 0.928109984 Simplifying x = 0.928109984Subproblem 2
x + 4.6 = -5.528109984 Simplifying x + 4.6 = -5.528109984 Reorder the terms: 4.6 + x = -5.528109984 Solving 4.6 + x = -5.528109984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6' to each side of the equation. 4.6 + -4.6 + x = -5.528109984 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + x = -5.528109984 + -4.6 x = -5.528109984 + -4.6 Combine like terms: -5.528109984 + -4.6 = -10.128109984 x = -10.128109984 Simplifying x = -10.128109984Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.928109984, -10.128109984}
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