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Simplifying 0 = -20x2 + 300x + 147 Reorder the terms: 0 = 147 + 300x + -20x2 Solving 0 = 147 + 300x + -20x2 Solving for variable 'x'. Combine like terms: 0 + -147 = -147 -147 + -300x + 20x2 = 147 + 300x + -20x2 + -147 + -300x + 20x2 Reorder the terms: -147 + -300x + 20x2 = 147 + -147 + 300x + -300x + -20x2 + 20x2 Combine like terms: 147 + -147 = 0 -147 + -300x + 20x2 = 0 + 300x + -300x + -20x2 + 20x2 -147 + -300x + 20x2 = 300x + -300x + -20x2 + 20x2 Combine like terms: 300x + -300x = 0 -147 + -300x + 20x2 = 0 + -20x2 + 20x2 -147 + -300x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -147 + -300x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -7.35 + -15x + x2 = 0 Move the constant term to the right: Add '7.35' to each side of the equation. -7.35 + -15x + 7.35 + x2 = 0 + 7.35 Reorder the terms: -7.35 + 7.35 + -15x + x2 = 0 + 7.35 Combine like terms: -7.35 + 7.35 = 0.00 0.00 + -15x + x2 = 0 + 7.35 -15x + x2 = 0 + 7.35 Combine like terms: 0 + 7.35 = 7.35 -15x + x2 = 7.35 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 7.35 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 7.35 + 56.25 Combine like terms: 7.35 + 56.25 = 63.6 56.25 + -15x + x2 = 63.6 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 63.6 Calculate the square root of the right side: 7.974960815 Break this problem into two subproblems by setting (x + -7.5) equal to 7.974960815 and -7.974960815.Subproblem 1
x + -7.5 = 7.974960815 Simplifying x + -7.5 = 7.974960815 Reorder the terms: -7.5 + x = 7.974960815 Solving -7.5 + x = 7.974960815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.974960815 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.974960815 + 7.5 x = 7.974960815 + 7.5 Combine like terms: 7.974960815 + 7.5 = 15.474960815 x = 15.474960815 Simplifying x = 15.474960815Subproblem 2
x + -7.5 = -7.974960815 Simplifying x + -7.5 = -7.974960815 Reorder the terms: -7.5 + x = -7.974960815 Solving -7.5 + x = -7.974960815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.974960815 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.974960815 + 7.5 x = -7.974960815 + 7.5 Combine like terms: -7.974960815 + 7.5 = -0.474960815 x = -0.474960815 Simplifying x = -0.474960815Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.474960815, -0.474960815}
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