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Simplifying 9(5x2 + -7x + 1) = 0 Reorder the terms: 9(1 + -7x + 5x2) = 0 (1 * 9 + -7x * 9 + 5x2 * 9) = 0 (9 + -63x + 45x2) = 0 Solving 9 + -63x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + -7x + 5x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + -7x + 5x2 = 0 Solving 1 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.4x + x2 = 0 + -0.2 -1.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.4x + x2 = -0.2 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.2 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.2 + 0.49 Combine like terms: -0.2 + 0.49 = 0.29 0.49 + -1.4x + x2 = 0.29 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + -0.7) equal to 0.538516481 and -0.538516481.Subproblem 1
x + -0.7 = 0.538516481 Simplifying x + -0.7 = 0.538516481 Reorder the terms: -0.7 + x = 0.538516481 Solving -0.7 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.538516481 + 0.7 x = 0.538516481 + 0.7 Combine like terms: 0.538516481 + 0.7 = 1.238516481 x = 1.238516481 Simplifying x = 1.238516481Subproblem 2
x + -0.7 = -0.538516481 Simplifying x + -0.7 = -0.538516481 Reorder the terms: -0.7 + x = -0.538516481 Solving -0.7 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.538516481 + 0.7 x = -0.538516481 + 0.7 Combine like terms: -0.538516481 + 0.7 = 0.161483519 x = 0.161483519 Simplifying x = 0.161483519Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.238516481, 0.161483519}Solution
x = {1.238516481, 0.161483519}
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