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Simplifying -4x2 + 15x + 7 = 0 Reorder the terms: 7 + 15x + -4x2 = 0 Solving 7 + 15x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -3.75x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -3.75x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -3.75x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -3.75x + x2 = 0 + 1.75 -3.75x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -3.75x + x2 = 1.75 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 = 1.75 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 1.75 + 3.515625 Combine like terms: 1.75 + 3.515625 = 5.265625 3.515625 + -3.75x + x2 = 5.265625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (x + -1.875) equal to 2.294694969 and -2.294694969.Subproblem 1
x + -1.875 = 2.294694969 Simplifying x + -1.875 = 2.294694969 Reorder the terms: -1.875 + x = 2.294694969 Solving -1.875 + x = 2.294694969 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 = 2.294694969 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.294694969 + 1.875 x = 2.294694969 + 1.875 Combine like terms: 2.294694969 + 1.875 = 4.169694969 x = 4.169694969 Simplifying x = 4.169694969Subproblem 2
x + -1.875 = -2.294694969 Simplifying x + -1.875 = -2.294694969 Reorder the terms: -1.875 + x = -2.294694969 Solving -1.875 + x = -2.294694969 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 = -2.294694969 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.294694969 + 1.875 x = -2.294694969 + 1.875 Combine like terms: -2.294694969 + 1.875 = -0.419694969 x = -0.419694969 Simplifying x = -0.419694969Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.169694969, -0.419694969}
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