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Simplifying 10x2 + 6x + 1 = 1225 Reorder the terms: 1 + 6x + 10x2 = 1225 Solving 1 + 6x + 10x2 = 1225 Solving for variable 'x'. Reorder the terms: 1 + -1225 + 6x + 10x2 = 1225 + -1225 Combine like terms: 1 + -1225 = -1224 -1224 + 6x + 10x2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1224 + 6x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-612 + 3x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-612 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying -612 + 3x + 5x2 = 0 Solving -612 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -122.4 + 0.6x + x2 = 0 Move the constant term to the right: Add '122.4' to each side of the equation. -122.4 + 0.6x + 122.4 + x2 = 0 + 122.4 Reorder the terms: -122.4 + 122.4 + 0.6x + x2 = 0 + 122.4 Combine like terms: -122.4 + 122.4 = 0.0 0.0 + 0.6x + x2 = 0 + 122.4 0.6x + x2 = 0 + 122.4 Combine like terms: 0 + 122.4 = 122.4 0.6x + x2 = 122.4 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 122.4 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 122.4 + 0.09 Combine like terms: 122.4 + 0.09 = 122.49 0.09 + 0.6x + x2 = 122.49 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 122.49 Calculate the square root of the right side: 11.067520047 Break this problem into two subproblems by setting (x + 0.3) equal to 11.067520047 and -11.067520047.Subproblem 1
x + 0.3 = 11.067520047 Simplifying x + 0.3 = 11.067520047 Reorder the terms: 0.3 + x = 11.067520047 Solving 0.3 + x = 11.067520047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 11.067520047 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 11.067520047 + -0.3 x = 11.067520047 + -0.3 Combine like terms: 11.067520047 + -0.3 = 10.767520047 x = 10.767520047 Simplifying x = 10.767520047Subproblem 2
x + 0.3 = -11.067520047 Simplifying x + 0.3 = -11.067520047 Reorder the terms: 0.3 + x = -11.067520047 Solving 0.3 + x = -11.067520047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -11.067520047 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -11.067520047 + -0.3 x = -11.067520047 + -0.3 Combine like terms: -11.067520047 + -0.3 = -11.367520047 x = -11.367520047 Simplifying x = -11.367520047Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.767520047, -11.367520047}Solution
x = {10.767520047, -11.367520047}
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