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Simplifying 4x2 + 15x + -15 = 0 Reorder the terms: -15 + 15x + 4x2 = 0 Solving -15 + 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'. -3.75 + 3.75x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 3.75x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 3.75x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 3.75x + x2 = 0 + 3.75 3.75x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 3.75x + x2 = 3.75 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 = 3.75 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 3.75 + 3.515625 Combine like terms: 3.75 + 3.515625 = 7.265625 3.515625 + 3.75x + x2 = 7.265625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 7.265625 Calculate the square root of the right side: 2.695482332 Break this problem into two subproblems by setting (x + 1.875) equal to 2.695482332 and -2.695482332.Subproblem 1
x + 1.875 = 2.695482332 Simplifying x + 1.875 = 2.695482332 Reorder the terms: 1.875 + x = 2.695482332 Solving 1.875 + x = 2.695482332 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 = 2.695482332 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.695482332 + -1.875 x = 2.695482332 + -1.875 Combine like terms: 2.695482332 + -1.875 = 0.820482332 x = 0.820482332 Simplifying x = 0.820482332Subproblem 2
x + 1.875 = -2.695482332 Simplifying x + 1.875 = -2.695482332 Reorder the terms: 1.875 + x = -2.695482332 Solving 1.875 + x = -2.695482332 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 = -2.695482332 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.695482332 + -1.875 x = -2.695482332 + -1.875 Combine like terms: -2.695482332 + -1.875 = -4.570482332 x = -4.570482332 Simplifying x = -4.570482332Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.820482332, -4.570482332}
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