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Simplifying 7 = 8(x + 5) * 5x Reorder the terms: 7 = 8(5 + x) * 5x Reorder the terms for easier multiplication: 7 = 8 * 5x(5 + x) Multiply 8 * 5 7 = 40x(5 + x) 7 = (5 * 40x + x * 40x) 7 = (200x + 40x2) Solving 7 = 200x + 40x2 Solving for variable 'x'. Reorder the terms: 7 + -200x + -40x2 = 200x + -200x + 40x2 + -40x2 Combine like terms: 200x + -200x = 0 7 + -200x + -40x2 = 0 + 40x2 + -40x2 7 + -200x + -40x2 = 40x2 + -40x2 Combine like terms: 40x2 + -40x2 = 0 7 + -200x + -40x2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.175 + 5x + x2 = 0 Move the constant term to the right: Add '0.175' to each side of the equation. -0.175 + 5x + 0.175 + x2 = 0 + 0.175 Reorder the terms: -0.175 + 0.175 + 5x + x2 = 0 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + 5x + x2 = 0 + 0.175 5x + x2 = 0 + 0.175 Combine like terms: 0 + 0.175 = 0.175 5x + x2 = 0.175 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.175 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.175 + 6.25 Combine like terms: 0.175 + 6.25 = 6.425 6.25 + 5x + x2 = 6.425 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.425 Calculate the square root of the right side: 2.534758371 Break this problem into two subproblems by setting (x + 2.5) equal to 2.534758371 and -2.534758371.Subproblem 1
x + 2.5 = 2.534758371 Simplifying x + 2.5 = 2.534758371 Reorder the terms: 2.5 + x = 2.534758371 Solving 2.5 + x = 2.534758371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.534758371 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.534758371 + -2.5 x = 2.534758371 + -2.5 Combine like terms: 2.534758371 + -2.5 = 0.034758371 x = 0.034758371 Simplifying x = 0.034758371Subproblem 2
x + 2.5 = -2.534758371 Simplifying x + 2.5 = -2.534758371 Reorder the terms: 2.5 + x = -2.534758371 Solving 2.5 + x = -2.534758371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.534758371 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.534758371 + -2.5 x = -2.534758371 + -2.5 Combine like terms: -2.534758371 + -2.5 = -5.034758371 x = -5.034758371 Simplifying x = -5.034758371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.034758371, -5.034758371}
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