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Simplifying 10x2 + -144x + 336 = 0 Reorder the terms: 336 + -144x + 10x2 = 0 Solving 336 + -144x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(168 + -72x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(168 + -72x + 5x2)' equal to zero and attempt to solve: Simplifying 168 + -72x + 5x2 = 0 Solving 168 + -72x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 33.6 + -14.4x + x2 = 0 Move the constant term to the right: Add '-33.6' to each side of the equation. 33.6 + -14.4x + -33.6 + x2 = 0 + -33.6 Reorder the terms: 33.6 + -33.6 + -14.4x + x2 = 0 + -33.6 Combine like terms: 33.6 + -33.6 = 0.0 0.0 + -14.4x + x2 = 0 + -33.6 -14.4x + x2 = 0 + -33.6 Combine like terms: 0 + -33.6 = -33.6 -14.4x + x2 = -33.6 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = -33.6 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = -33.6 + 51.84 Combine like terms: -33.6 + 51.84 = 18.24 51.84 + -14.4x + x2 = 18.24 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 18.24 Calculate the square root of the right side: 4.270831301 Break this problem into two subproblems by setting (x + -7.2) equal to 4.270831301 and -4.270831301.Subproblem 1
x + -7.2 = 4.270831301 Simplifying x + -7.2 = 4.270831301 Reorder the terms: -7.2 + x = 4.270831301 Solving -7.2 + x = 4.270831301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = 4.270831301 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 4.270831301 + 7.2 x = 4.270831301 + 7.2 Combine like terms: 4.270831301 + 7.2 = 11.470831301 x = 11.470831301 Simplifying x = 11.470831301Subproblem 2
x + -7.2 = -4.270831301 Simplifying x + -7.2 = -4.270831301 Reorder the terms: -7.2 + x = -4.270831301 Solving -7.2 + x = -4.270831301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = -4.270831301 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -4.270831301 + 7.2 x = -4.270831301 + 7.2 Combine like terms: -4.270831301 + 7.2 = 2.929168699 x = 2.929168699 Simplifying x = 2.929168699Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.470831301, 2.929168699}Solution
x = {11.470831301, 2.929168699}
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