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Simplifying 25x2 + -170x + 289 = 54 Reorder the terms: 289 + -170x + 25x2 = 54 Solving 289 + -170x + 25x2 = 54 Solving for variable 'x'. Reorder the terms: 289 + -54 + -170x + 25x2 = 54 + -54 Combine like terms: 289 + -54 = 235 235 + -170x + 25x2 = 54 + -54 Combine like terms: 54 + -54 = 0 235 + -170x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(47 + -34x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(47 + -34x + 5x2)' equal to zero and attempt to solve: Simplifying 47 + -34x + 5x2 = 0 Solving 47 + -34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 9.4 + -6.8x + x2 = 0 Move the constant term to the right: Add '-9.4' to each side of the equation. 9.4 + -6.8x + -9.4 + x2 = 0 + -9.4 Reorder the terms: 9.4 + -9.4 + -6.8x + x2 = 0 + -9.4 Combine like terms: 9.4 + -9.4 = 0.0 0.0 + -6.8x + x2 = 0 + -9.4 -6.8x + x2 = 0 + -9.4 Combine like terms: 0 + -9.4 = -9.4 -6.8x + x2 = -9.4 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = -9.4 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = -9.4 + 11.56 Combine like terms: -9.4 + 11.56 = 2.16 11.56 + -6.8x + x2 = 2.16 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + -3.4) equal to 1.469693846 and -1.469693846.Subproblem 1
x + -3.4 = 1.469693846 Simplifying x + -3.4 = 1.469693846 Reorder the terms: -3.4 + x = 1.469693846 Solving -3.4 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 1.469693846 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 1.469693846 + 3.4 x = 1.469693846 + 3.4 Combine like terms: 1.469693846 + 3.4 = 4.869693846 x = 4.869693846 Simplifying x = 4.869693846Subproblem 2
x + -3.4 = -1.469693846 Simplifying x + -3.4 = -1.469693846 Reorder the terms: -3.4 + x = -1.469693846 Solving -3.4 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -1.469693846 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -1.469693846 + 3.4 x = -1.469693846 + 3.4 Combine like terms: -1.469693846 + 3.4 = 1.930306154 x = 1.930306154 Simplifying x = 1.930306154Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.869693846, 1.930306154}Solution
x = {4.869693846, 1.930306154}
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