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Simplifying 3x2 + -15x + x2 + -7 = 180 Reorder the terms: -7 + -15x + 3x2 + x2 = 180 Combine like terms: 3x2 + x2 = 4x2 -7 + -15x + 4x2 = 180 Solving -7 + -15x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -7 + -180 + -15x + 4x2 = 180 + -180 Combine like terms: -7 + -180 = -187 -187 + -15x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -187 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -46.75 + -3.75x + x2 = 0 Move the constant term to the right: Add '46.75' to each side of the equation. -46.75 + -3.75x + 46.75 + x2 = 0 + 46.75 Reorder the terms: -46.75 + 46.75 + -3.75x + x2 = 0 + 46.75 Combine like terms: -46.75 + 46.75 = 0.00 0.00 + -3.75x + x2 = 0 + 46.75 -3.75x + x2 = 0 + 46.75 Combine like terms: 0 + 46.75 = 46.75 -3.75x + x2 = 46.75 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 46.75 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 46.75 + 3.515625 Combine like terms: 46.75 + 3.515625 = 50.265625 3.515625 + -3.75x + x2 = 50.265625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 50.265625 Calculate the square root of the right side: 7.089825456 Break this problem into two subproblems by setting (x + -1.875) equal to 7.089825456 and -7.089825456.Subproblem 1
x + -1.875 = 7.089825456 Simplifying x + -1.875 = 7.089825456 Reorder the terms: -1.875 + x = 7.089825456 Solving -1.875 + x = 7.089825456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 7.089825456 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 7.089825456 + 1.875 x = 7.089825456 + 1.875 Combine like terms: 7.089825456 + 1.875 = 8.964825456 x = 8.964825456 Simplifying x = 8.964825456Subproblem 2
x + -1.875 = -7.089825456 Simplifying x + -1.875 = -7.089825456 Reorder the terms: -1.875 + x = -7.089825456 Solving -1.875 + x = -7.089825456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -7.089825456 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -7.089825456 + 1.875 x = -7.089825456 + 1.875 Combine like terms: -7.089825456 + 1.875 = -5.214825456 x = -5.214825456 Simplifying x = -5.214825456Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.964825456, -5.214825456}
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