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Simplifying 7056 = (x + 3)(x + -1) Reorder the terms: 7056 = (3 + x)(x + -1) Reorder the terms: 7056 = (3 + x)(-1 + x) Multiply (3 + x) * (-1 + x) 7056 = (3(-1 + x) + x(-1 + x)) 7056 = ((-1 * 3 + x * 3) + x(-1 + x)) 7056 = ((-3 + 3x) + x(-1 + x)) 7056 = (-3 + 3x + (-1 * x + x * x)) 7056 = (-3 + 3x + (-1x + x2)) Combine like terms: 3x + -1x = 2x 7056 = (-3 + 2x + x2) Solving 7056 = -3 + 2x + x2 Solving for variable 'x'. Combine like terms: 7056 + 3 = 7059 7059 + -2x + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2 Reorder the terms: 7059 + -2x + -1x2 = -3 + 3 + 2x + -2x + x2 + -1x2 Combine like terms: -3 + 3 = 0 7059 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 7059 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 7059 + -2x + -1x2 = 0 + x2 + -1x2 7059 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7059 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7059 + 2x + x2 = 0 Move the constant term to the right: Add '7059' to each side of the equation. -7059 + 2x + 7059 + x2 = 0 + 7059 Reorder the terms: -7059 + 7059 + 2x + x2 = 0 + 7059 Combine like terms: -7059 + 7059 = 0 0 + 2x + x2 = 0 + 7059 2x + x2 = 0 + 7059 Combine like terms: 0 + 7059 = 7059 2x + x2 = 7059 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 7059 + 1 Reorder the terms: 1 + 2x + x2 = 7059 + 1 Combine like terms: 7059 + 1 = 7060 1 + 2x + x2 = 7060 Factor a perfect square on the left side: (x + 1)(x + 1) = 7060 Calculate the square root of the right side: 84.02380615 Break this problem into two subproblems by setting (x + 1) equal to 84.02380615 and -84.02380615.Subproblem 1
x + 1 = 84.02380615 Simplifying x + 1 = 84.02380615 Reorder the terms: 1 + x = 84.02380615 Solving 1 + x = 84.02380615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 84.02380615 + -1 Combine like terms: 1 + -1 = 0 0 + x = 84.02380615 + -1 x = 84.02380615 + -1 Combine like terms: 84.02380615 + -1 = 83.02380615 x = 83.02380615 Simplifying x = 83.02380615Subproblem 2
x + 1 = -84.02380615 Simplifying x + 1 = -84.02380615 Reorder the terms: 1 + x = -84.02380615 Solving 1 + x = -84.02380615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -84.02380615 + -1 Combine like terms: 1 + -1 = 0 0 + x = -84.02380615 + -1 x = -84.02380615 + -1 Combine like terms: -84.02380615 + -1 = -85.02380615 x = -85.02380615 Simplifying x = -85.02380615Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.02380615, -85.02380615}
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