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Simplifying 24x2 + -72x + 28 = 0 Reorder the terms: 28 + -72x + 24x2 = 0 Solving 28 + -72x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -18x + 6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -18x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + -18x + 6x2 = 0 Solving 7 + -18x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + -3x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -3x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -3x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + -1.166666667 -3x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -3x + x2 = -1.166666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.166666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.166666667 + 2.25 Combine like terms: -1.166666667 + 2.25 = 1.083333333 2.25 + -3x + x2 = 1.083333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.083333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (x + -1.5) equal to 1.040833 and -1.040833.Subproblem 1
x + -1.5 = 1.040833 Simplifying x + -1.5 = 1.040833 Reorder the terms: -1.5 + x = 1.040833 Solving -1.5 + x = 1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.040833 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.040833 + 1.5 x = 1.040833 + 1.5 Combine like terms: 1.040833 + 1.5 = 2.540833 x = 2.540833 Simplifying x = 2.540833Subproblem 2
x + -1.5 = -1.040833 Simplifying x + -1.5 = -1.040833 Reorder the terms: -1.5 + x = -1.040833 Solving -1.5 + x = -1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.040833 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.040833 + 1.5 x = -1.040833 + 1.5 Combine like terms: -1.040833 + 1.5 = 0.459167 x = 0.459167 Simplifying x = 0.459167Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.540833, 0.459167}Solution
x = {2.540833, 0.459167}
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