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Simplifying 7(25x2 + -60x + 36) + -119 = 0 Reorder the terms: 7(36 + -60x + 25x2) + -119 = 0 (36 * 7 + -60x * 7 + 25x2 * 7) + -119 = 0 (252 + -420x + 175x2) + -119 = 0 Reorder the terms: 252 + -119 + -420x + 175x2 = 0 Combine like terms: 252 + -119 = 133 133 + -420x + 175x2 = 0 Solving 133 + -420x + 175x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(19 + -60x + 25x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(19 + -60x + 25x2)' equal to zero and attempt to solve: Simplifying 19 + -60x + 25x2 = 0 Solving 19 + -60x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.76 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.76' to each side of the equation. 0.76 + -2.4x + -0.76 + x2 = 0 + -0.76 Reorder the terms: 0.76 + -0.76 + -2.4x + x2 = 0 + -0.76 Combine like terms: 0.76 + -0.76 = 0.00 0.00 + -2.4x + x2 = 0 + -0.76 -2.4x + x2 = 0 + -0.76 Combine like terms: 0 + -0.76 = -0.76 -2.4x + x2 = -0.76 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.76 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.76 + 1.44 Combine like terms: -0.76 + 1.44 = 0.68 1.44 + -2.4x + x2 = 0.68 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.68 Calculate the square root of the right side: 0.824621125 Break this problem into two subproblems by setting (x + -1.2) equal to 0.824621125 and -0.824621125.Subproblem 1
x + -1.2 = 0.824621125 Simplifying x + -1.2 = 0.824621125 Reorder the terms: -1.2 + x = 0.824621125 Solving -1.2 + x = 0.824621125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.824621125 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.824621125 + 1.2 x = 0.824621125 + 1.2 Combine like terms: 0.824621125 + 1.2 = 2.024621125 x = 2.024621125 Simplifying x = 2.024621125Subproblem 2
x + -1.2 = -0.824621125 Simplifying x + -1.2 = -0.824621125 Reorder the terms: -1.2 + x = -0.824621125 Solving -1.2 + x = -0.824621125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.824621125 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.824621125 + 1.2 x = -0.824621125 + 1.2 Combine like terms: -0.824621125 + 1.2 = 0.375378875 x = 0.375378875 Simplifying x = 0.375378875Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.024621125, 0.375378875}Solution
x = {2.024621125, 0.375378875}
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