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Simplifying (-4x + 15) = (8x2 + 24x) Reorder the terms: (15 + -4x) = (8x2 + 24x) Remove parenthesis around (15 + -4x) 15 + -4x = (8x2 + 24x) Reorder the terms: 15 + -4x = (24x + 8x2) Remove parenthesis around (24x + 8x2) 15 + -4x = 24x + 8x2 Solving 15 + -4x = 24x + 8x2 Solving for variable 'x'. Combine like terms: -4x + -24x = -28x 15 + -28x + -8x2 = 24x + 8x2 + -24x + -8x2 Reorder the terms: 15 + -28x + -8x2 = 24x + -24x + 8x2 + -8x2 Combine like terms: 24x + -24x = 0 15 + -28x + -8x2 = 0 + 8x2 + -8x2 15 + -28x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 15 + -28x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + 3.5x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 3.5x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 3.5x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 3.5x + x2 = 0 + 1.875 3.5x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 3.5x + x2 = 1.875 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 1.875 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 1.875 + 3.0625 Combine like terms: 1.875 + 3.0625 = 4.9375 3.0625 + 3.5x + x2 = 4.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 4.9375 Calculate the square root of the right side: 2.222048604 Break this problem into two subproblems by setting (x + 1.75) equal to 2.222048604 and -2.222048604.Subproblem 1
x + 1.75 = 2.222048604 Simplifying x + 1.75 = 2.222048604 Reorder the terms: 1.75 + x = 2.222048604 Solving 1.75 + x = 2.222048604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.222048604 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.222048604 + -1.75 x = 2.222048604 + -1.75 Combine like terms: 2.222048604 + -1.75 = 0.472048604 x = 0.472048604 Simplifying x = 0.472048604Subproblem 2
x + 1.75 = -2.222048604 Simplifying x + 1.75 = -2.222048604 Reorder the terms: 1.75 + x = -2.222048604 Solving 1.75 + x = -2.222048604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.222048604 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.222048604 + -1.75 x = -2.222048604 + -1.75 Combine like terms: -2.222048604 + -1.75 = -3.972048604 x = -3.972048604 Simplifying x = -3.972048604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.472048604, -3.972048604}
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