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Simplifying 63 = 0.5(2x)(2x + 4) Remove parenthesis around (2x) 63 = 0.5 * 2x(2x + 4) Reorder the terms: 63 = 0.5 * 2x(4 + 2x) Multiply 0.5 * 2 63 = 1x(4 + 2x) 63 = (4 * 1x + 2x * 1x) 63 = (4x + 2x2) Solving 63 = 4x + 2x2 Solving for variable 'x'. Reorder the terms: 63 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 63 + -4x + -2x2 = 0 + 2x2 + -2x2 63 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 63 + -4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -31.5 + 2x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 2x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 2x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 2x + x2 = 0 + 31.5 2x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 2x + x2 = 31.5 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 = 31.5 + 1 Reorder the terms: 1 + 2x + x2 = 31.5 + 1 Combine like terms: 31.5 + 1 = 32.5 1 + 2x + x2 = 32.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (x + 1) equal to 5.700877125 and -5.700877125.Subproblem 1
x + 1 = 5.700877125 Simplifying x + 1 = 5.700877125 Reorder the terms: 1 + x = 5.700877125 Solving 1 + x = 5.700877125 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 = 5.700877125 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.700877125 + -1 x = 5.700877125 + -1 Combine like terms: 5.700877125 + -1 = 4.700877125 x = 4.700877125 Simplifying x = 4.700877125Subproblem 2
x + 1 = -5.700877125 Simplifying x + 1 = -5.700877125 Reorder the terms: 1 + x = -5.700877125 Solving 1 + x = -5.700877125 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 = -5.700877125 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.700877125 + -1 x = -5.700877125 + -1 Combine like terms: -5.700877125 + -1 = -6.700877125 x = -6.700877125 Simplifying x = -6.700877125Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.700877125, -6.700877125}
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