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Simplifying 6x + -0.75 = x2 Reorder the terms: -0.75 + 6x = x2 Solving -0.75 + 6x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -0.75 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.75 + -6x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -6x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -6x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -6x + x2 = 0 + -0.75 -6x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -6x + x2 = -0.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.75 + 9 Reorder the terms: 9 + -6x + x2 = -0.75 + 9 Combine like terms: -0.75 + 9 = 8.25 9 + -6x + x2 = 8.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -3) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -3 = 2.872281323 Simplifying x + -3 = 2.872281323 Reorder the terms: -3 + x = 2.872281323 Solving -3 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.872281323 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.872281323 + 3 x = 2.872281323 + 3 Combine like terms: 2.872281323 + 3 = 5.872281323 x = 5.872281323 Simplifying x = 5.872281323Subproblem 2
x + -3 = -2.872281323 Simplifying x + -3 = -2.872281323 Reorder the terms: -3 + x = -2.872281323 Solving -3 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.872281323 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.872281323 + 3 x = -2.872281323 + 3 Combine like terms: -2.872281323 + 3 = 0.127718677 x = 0.127718677 Simplifying x = 0.127718677Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.872281323, 0.127718677}
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