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Simplifying x(x + 7) = 50 Reorder the terms: x(7 + x) = 50 (7 * x + x * x) = 50 (7x + x2) = 50 Solving 7x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 7x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 7x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 7x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 7x + x2 = 0 + 50 7x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 7x + x2 = 50 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 50 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 50 + 12.25 Combine like terms: 50 + 12.25 = 62.25 12.25 + 7x + x2 = 62.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 3.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 3.5 = 7.889866919 Simplifying x + 3.5 = 7.889866919 Reorder the terms: 3.5 + x = 7.889866919 Solving 3.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.889866919 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.889866919 + -3.5 x = 7.889866919 + -3.5 Combine like terms: 7.889866919 + -3.5 = 4.389866919 x = 4.389866919 Simplifying x = 4.389866919Subproblem 2
x + 3.5 = -7.889866919 Simplifying x + 3.5 = -7.889866919 Reorder the terms: 3.5 + x = -7.889866919 Solving 3.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.889866919 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.889866919 + -3.5 x = -7.889866919 + -3.5 Combine like terms: -7.889866919 + -3.5 = -11.389866919 x = -11.389866919 Simplifying x = -11.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.389866919, -11.389866919}
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