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Simplifying 10x2 + -144x + 14 = 0 Reorder the terms: 14 + -144x + 10x2 = 0 Solving 14 + -144x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -72x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -72x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + -72x + 5x2 = 0 Solving 7 + -72x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -14.4x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -14.4x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -14.4x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -14.4x + x2 = 0 + -1.4 -14.4x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -14.4x + x2 = -1.4 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 = -1.4 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = -1.4 + 51.84 Combine like terms: -1.4 + 51.84 = 50.44 51.84 + -14.4x + x2 = 50.44 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 50.44 Calculate the square root of the right side: 7.102112362 Break this problem into two subproblems by setting (x + -7.2) equal to 7.102112362 and -7.102112362.Subproblem 1
x + -7.2 = 7.102112362 Simplifying x + -7.2 = 7.102112362 Reorder the terms: -7.2 + x = 7.102112362 Solving -7.2 + x = 7.102112362 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 = 7.102112362 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 7.102112362 + 7.2 x = 7.102112362 + 7.2 Combine like terms: 7.102112362 + 7.2 = 14.302112362 x = 14.302112362 Simplifying x = 14.302112362Subproblem 2
x + -7.2 = -7.102112362 Simplifying x + -7.2 = -7.102112362 Reorder the terms: -7.2 + x = -7.102112362 Solving -7.2 + x = -7.102112362 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 = -7.102112362 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -7.102112362 + 7.2 x = -7.102112362 + 7.2 Combine like terms: -7.102112362 + 7.2 = 0.097887638 x = 0.097887638 Simplifying x = 0.097887638Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.302112362, 0.097887638}Solution
x = {14.302112362, 0.097887638}
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