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Simplifying 84 = (x)(x + 4) Reorder the terms: 84 = x(4 + x) 84 = (4 * x + x * x) 84 = (4x + x2) Solving 84 = 4x + x2 Solving for variable 'x'. Reorder the terms: 84 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 84 + -4x + -1x2 = 0 + x2 + -1x2 84 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 84 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -84 + 4x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + 4x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 4x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 4x + x2 = 0 + 84 4x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 4x + x2 = 84 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 84 + 4 Reorder the terms: 4 + 4x + x2 = 84 + 4 Combine like terms: 84 + 4 = 88 4 + 4x + x2 = 88 Factor a perfect square on the left side: (x + 2)(x + 2) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 2) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 2 = 9.38083152 Simplifying x + 2 = 9.38083152 Reorder the terms: 2 + x = 9.38083152 Solving 2 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.38083152 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.38083152 + -2 x = 9.38083152 + -2 Combine like terms: 9.38083152 + -2 = 7.38083152 x = 7.38083152 Simplifying x = 7.38083152Subproblem 2
x + 2 = -9.38083152 Simplifying x + 2 = -9.38083152 Reorder the terms: 2 + x = -9.38083152 Solving 2 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.38083152 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.38083152 + -2 x = -9.38083152 + -2 Combine like terms: -9.38083152 + -2 = -11.38083152 x = -11.38083152 Simplifying x = -11.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.38083152, -11.38083152}
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