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Simplifying 0 = 4x2 + 15x + -8 Reorder the terms: 0 = -8 + 15x + 4x2 Solving 0 = -8 + 15x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + -15x + -4x2 = -8 + 15x + 4x2 + 8 + -15x + -4x2 Reorder the terms: 8 + -15x + -4x2 = -8 + 8 + 15x + -15x + 4x2 + -4x2 Combine like terms: -8 + 8 = 0 8 + -15x + -4x2 = 0 + 15x + -15x + 4x2 + -4x2 8 + -15x + -4x2 = 15x + -15x + 4x2 + -4x2 Combine like terms: 15x + -15x = 0 8 + -15x + -4x2 = 0 + 4x2 + -4x2 8 + -15x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + -15x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + 3.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.75x + x2 = 0 + 2 3.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.75x + x2 = 2 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 = 2 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 2 + 3.515625 Combine like terms: 2 + 3.515625 = 5.515625 3.515625 + 3.75x + x2 = 5.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 5.515625 Calculate the square root of the right side: 2.348536779 Break this problem into two subproblems by setting (x + 1.875) equal to 2.348536779 and -2.348536779.Subproblem 1
x + 1.875 = 2.348536779 Simplifying x + 1.875 = 2.348536779 Reorder the terms: 1.875 + x = 2.348536779 Solving 1.875 + x = 2.348536779 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 = 2.348536779 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.348536779 + -1.875 x = 2.348536779 + -1.875 Combine like terms: 2.348536779 + -1.875 = 0.473536779 x = 0.473536779 Simplifying x = 0.473536779Subproblem 2
x + 1.875 = -2.348536779 Simplifying x + 1.875 = -2.348536779 Reorder the terms: 1.875 + x = -2.348536779 Solving 1.875 + x = -2.348536779 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 = -2.348536779 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.348536779 + -1.875 x = -2.348536779 + -1.875 Combine like terms: -2.348536779 + -1.875 = -4.223536779 x = -4.223536779 Simplifying x = -4.223536779Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.473536779, -4.223536779}
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