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Simplifying 6x2 + 2.5x + -1.5 = 0 Reorder the terms: -1.5 + 2.5x + 6x2 = 0 Solving -1.5 + 2.5x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.25 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.4166666667x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.4166666667x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.4166666667x + x2 = 0 + 0.25 0.4166666667x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.4166666667x + x2 = 0.25 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 0.25 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 0.25 + 0.04340277781 Combine like terms: 0.25 + 0.04340277781 = 0.29340277781 0.04340277781 + 0.4166666667x + x2 = 0.29340277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 0.29340277781 Calculate the square root of the right side: 0.541666667 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 0.541666667 and -0.541666667.Subproblem 1
x + 0.2083333334 = 0.541666667 Simplifying x + 0.2083333334 = 0.541666667 Reorder the terms: 0.2083333334 + x = 0.541666667 Solving 0.2083333334 + x = 0.541666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 0.541666667 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 0.541666667 + -0.2083333334 x = 0.541666667 + -0.2083333334 Combine like terms: 0.541666667 + -0.2083333334 = 0.3333333336 x = 0.3333333336 Simplifying x = 0.3333333336Subproblem 2
x + 0.2083333334 = -0.541666667 Simplifying x + 0.2083333334 = -0.541666667 Reorder the terms: 0.2083333334 + x = -0.541666667 Solving 0.2083333334 + x = -0.541666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -0.541666667 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -0.541666667 + -0.2083333334 x = -0.541666667 + -0.2083333334 Combine like terms: -0.541666667 + -0.2083333334 = -0.7500000004 x = -0.7500000004 Simplifying x = -0.7500000004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3333333336, -0.7500000004}
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