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Simplifying 24x2 + -1x + -7 = 0 Reorder the terms: -7 + -1x + 24x2 = 0 Solving -7 + -1x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.2916666667 + -0.04166666667x + x2 = 0 Move the constant term to the right: Add '0.2916666667' to each side of the equation. -0.2916666667 + -0.04166666667x + 0.2916666667 + x2 = 0 + 0.2916666667 Reorder the terms: -0.2916666667 + 0.2916666667 + -0.04166666667x + x2 = 0 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + -0.04166666667x + x2 = 0 + 0.2916666667 -0.04166666667x + x2 = 0 + 0.2916666667 Combine like terms: 0 + 0.2916666667 = 0.2916666667 -0.04166666667x + x2 = 0.2916666667 The x term is -0.04166666667x. Take half its coefficient (-0.02083333334). Square it (0.0004340277781) and add it to both sides. Add '0.0004340277781' to each side of the equation. -0.04166666667x + 0.0004340277781 + x2 = 0.2916666667 + 0.0004340277781 Reorder the terms: 0.0004340277781 + -0.04166666667x + x2 = 0.2916666667 + 0.0004340277781 Combine like terms: 0.2916666667 + 0.0004340277781 = 0.2921006944781 0.0004340277781 + -0.04166666667x + x2 = 0.2921006944781 Factor a perfect square on the left side: (x + -0.02083333334)(x + -0.02083333334) = 0.2921006944781 Calculate the square root of the right side: 0.540463407 Break this problem into two subproblems by setting (x + -0.02083333334) equal to 0.540463407 and -0.540463407.Subproblem 1
x + -0.02083333334 = 0.540463407 Simplifying x + -0.02083333334 = 0.540463407 Reorder the terms: -0.02083333334 + x = 0.540463407 Solving -0.02083333334 + x = 0.540463407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02083333334' to each side of the equation. -0.02083333334 + 0.02083333334 + x = 0.540463407 + 0.02083333334 Combine like terms: -0.02083333334 + 0.02083333334 = 0.00000000000 0.00000000000 + x = 0.540463407 + 0.02083333334 x = 0.540463407 + 0.02083333334 Combine like terms: 0.540463407 + 0.02083333334 = 0.56129674034 x = 0.56129674034 Simplifying x = 0.56129674034Subproblem 2
x + -0.02083333334 = -0.540463407 Simplifying x + -0.02083333334 = -0.540463407 Reorder the terms: -0.02083333334 + x = -0.540463407 Solving -0.02083333334 + x = -0.540463407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02083333334' to each side of the equation. -0.02083333334 + 0.02083333334 + x = -0.540463407 + 0.02083333334 Combine like terms: -0.02083333334 + 0.02083333334 = 0.00000000000 0.00000000000 + x = -0.540463407 + 0.02083333334 x = -0.540463407 + 0.02083333334 Combine like terms: -0.540463407 + 0.02083333334 = -0.51963007366 x = -0.51963007366 Simplifying x = -0.51963007366Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.56129674034, -0.51963007366}
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