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Simplifying 6x2 + 25x + -4 = 0 Reorder the terms: -4 + 25x + 6x2 = 0 Solving -4 + 25x + 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'. -0.6666666667 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 4.166666667x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 4.166666667x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 4.166666667x + x2 = 0 + 0.6666666667 4.166666667x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 4.166666667x + x2 = 0.6666666667 The x term is 4.166666667x. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667x + 4.340277781 + x2 = 0.6666666667 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = 0.6666666667 + 4.340277781 Combine like terms: 0.6666666667 + 4.340277781 = 5.0069444477 4.340277781 + 4.166666667x + x2 = 5.0069444477 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 5.0069444477 Calculate the square root of the right side: 2.237620264 Break this problem into two subproblems by setting (x + 2.083333334) equal to 2.237620264 and -2.237620264.Subproblem 1
x + 2.083333334 = 2.237620264 Simplifying x + 2.083333334 = 2.237620264 Reorder the terms: 2.083333334 + x = 2.237620264 Solving 2.083333334 + x = 2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = 2.237620264 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 2.237620264 + -2.083333334 x = 2.237620264 + -2.083333334 Combine like terms: 2.237620264 + -2.083333334 = 0.15428693 x = 0.15428693 Simplifying x = 0.15428693Subproblem 2
x + 2.083333334 = -2.237620264 Simplifying x + 2.083333334 = -2.237620264 Reorder the terms: 2.083333334 + x = -2.237620264 Solving 2.083333334 + x = -2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = -2.237620264 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -2.237620264 + -2.083333334 x = -2.237620264 + -2.083333334 Combine like terms: -2.237620264 + -2.083333334 = -4.320953598 x = -4.320953598 Simplifying x = -4.320953598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.15428693, -4.320953598}
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