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Simplifying 8x2 + 30x + -75 = 0 Reorder the terms: -75 + 30x + 8x2 = 0 Solving -75 + 30x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.375 + 3.75x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 3.75x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 3.75x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 3.75x + x2 = 0 + 9.375 3.75x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 3.75x + x2 = 9.375 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 = 9.375 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 9.375 + 3.515625 Combine like terms: 9.375 + 3.515625 = 12.890625 3.515625 + 3.75x + x2 = 12.890625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 12.890625 Calculate the square root of the right side: 3.590351654 Break this problem into two subproblems by setting (x + 1.875) equal to 3.590351654 and -3.590351654.Subproblem 1
x + 1.875 = 3.590351654 Simplifying x + 1.875 = 3.590351654 Reorder the terms: 1.875 + x = 3.590351654 Solving 1.875 + x = 3.590351654 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 = 3.590351654 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 3.590351654 + -1.875 x = 3.590351654 + -1.875 Combine like terms: 3.590351654 + -1.875 = 1.715351654 x = 1.715351654 Simplifying x = 1.715351654Subproblem 2
x + 1.875 = -3.590351654 Simplifying x + 1.875 = -3.590351654 Reorder the terms: 1.875 + x = -3.590351654 Solving 1.875 + x = -3.590351654 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 = -3.590351654 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -3.590351654 + -1.875 x = -3.590351654 + -1.875 Combine like terms: -3.590351654 + -1.875 = -5.465351654 x = -5.465351654 Simplifying x = -5.465351654Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.715351654, -5.465351654}
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