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Simplifying 15 = 4x2 + -7x + 8 Reorder the terms: 15 = 8 + -7x + 4x2 Solving 15 = 8 + -7x + 4x2 Solving for variable 'x'. Combine like terms: 15 + -8 = 7 7 + 7x + -4x2 = 8 + -7x + 4x2 + -8 + 7x + -4x2 Reorder the terms: 7 + 7x + -4x2 = 8 + -8 + -7x + 7x + 4x2 + -4x2 Combine like terms: 8 + -8 = 0 7 + 7x + -4x2 = 0 + -7x + 7x + 4x2 + -4x2 7 + 7x + -4x2 = -7x + 7x + 4x2 + -4x2 Combine like terms: -7x + 7x = 0 7 + 7x + -4x2 = 0 + 4x2 + -4x2 7 + 7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 7 + 7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.75x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.75x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.75x + x2 = 0 + 1.75 -1.75x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.75x + x2 = 1.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 1.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 1.75 + 0.765625 Combine like terms: 1.75 + 0.765625 = 2.515625 0.765625 + -1.75x + x2 = 2.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + -0.875) equal to 1.586072193 and -1.586072193.Subproblem 1
x + -0.875 = 1.586072193 Simplifying x + -0.875 = 1.586072193 Reorder the terms: -0.875 + x = 1.586072193 Solving -0.875 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.586072193 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.586072193 + 0.875 x = 1.586072193 + 0.875 Combine like terms: 1.586072193 + 0.875 = 2.461072193 x = 2.461072193 Simplifying x = 2.461072193Subproblem 2
x + -0.875 = -1.586072193 Simplifying x + -0.875 = -1.586072193 Reorder the terms: -0.875 + x = -1.586072193 Solving -0.875 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.586072193 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.586072193 + 0.875 x = -1.586072193 + 0.875 Combine like terms: -1.586072193 + 0.875 = -0.711072193 x = -0.711072193 Simplifying x = -0.711072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.461072193, -0.711072193}
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