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Simplifying 0.875x2 + -5.25x + -152.25 = 0 Reorder the terms: -152.25 + -5.25x + 0.875x2 = 0 Solving -152.25 + -5.25x + 0.875x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.875 the coefficient of the squared term: Divide each side by '0.875'. -174 + -6x + x2 = 0 Move the constant term to the right: Add '174' to each side of the equation. -174 + -6x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + -6x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + -6x + x2 = 0 + 174 -6x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 -6x + x2 = 174 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 174 + 9 Reorder the terms: 9 + -6x + x2 = 174 + 9 Combine like terms: 174 + 9 = 183 9 + -6x + x2 = 183 Factor a perfect square on the left side: (x + -3)(x + -3) = 183 Calculate the square root of the right side: 13.527749258 Break this problem into two subproblems by setting (x + -3) equal to 13.527749258 and -13.527749258.Subproblem 1
x + -3 = 13.527749258 Simplifying x + -3 = 13.527749258 Reorder the terms: -3 + x = 13.527749258 Solving -3 + x = 13.527749258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 13.527749258 + 3 Combine like terms: -3 + 3 = 0 0 + x = 13.527749258 + 3 x = 13.527749258 + 3 Combine like terms: 13.527749258 + 3 = 16.527749258 x = 16.527749258 Simplifying x = 16.527749258Subproblem 2
x + -3 = -13.527749258 Simplifying x + -3 = -13.527749258 Reorder the terms: -3 + x = -13.527749258 Solving -3 + x = -13.527749258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -13.527749258 + 3 Combine like terms: -3 + 3 = 0 0 + x = -13.527749258 + 3 x = -13.527749258 + 3 Combine like terms: -13.527749258 + 3 = -10.527749258 x = -10.527749258 Simplifying x = -10.527749258Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.527749258, -10.527749258}
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