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Simplifying 65 = (x)(x + -3) Reorder the terms: 65 = x(-3 + x) 65 = (-3 * x + x * x) 65 = (-3x + x2) Solving 65 = -3x + x2 Solving for variable 'x'. Reorder the terms: 65 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 65 + 3x + -1x2 = 0 + x2 + -1x2 65 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 65 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -65 + -3x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + -3x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -3x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -3x + x2 = 0 + 65 -3x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -3x + x2 = 65 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 65 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 65 + 2.25 Combine like terms: 65 + 2.25 = 67.25 2.25 + -3x + x2 = 67.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + -1.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + -1.5 = 8.200609733 Simplifying x + -1.5 = 8.200609733 Reorder the terms: -1.5 + x = 8.200609733 Solving -1.5 + x = 8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 8.200609733 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.200609733 + 1.5 x = 8.200609733 + 1.5 Combine like terms: 8.200609733 + 1.5 = 9.700609733 x = 9.700609733 Simplifying x = 9.700609733Subproblem 2
x + -1.5 = -8.200609733 Simplifying x + -1.5 = -8.200609733 Reorder the terms: -1.5 + x = -8.200609733 Solving -1.5 + x = -8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -8.200609733 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.200609733 + 1.5 x = -8.200609733 + 1.5 Combine like terms: -8.200609733 + 1.5 = -6.700609733 x = -6.700609733 Simplifying x = -6.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.700609733, -6.700609733}
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