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Simplifying 2x2 + 4x(10) = 6250 Reorder the terms for easier multiplication: 2x2 + 4 * 10x = 6250 Multiply 4 * 10 2x2 + 40x = 6250 Reorder the terms: 40x + 2x2 = 6250 Solving 40x + 2x2 = 6250 Solving for variable 'x'. Reorder the terms: -6250 + 40x + 2x2 = 6250 + -6250 Combine like terms: 6250 + -6250 = 0 -6250 + 40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3125 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3125 + 20x + x2)' equal to zero and attempt to solve: Simplifying -3125 + 20x + x2 = 0 Solving -3125 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3125' to each side of the equation. -3125 + 20x + 3125 + x2 = 0 + 3125 Reorder the terms: -3125 + 3125 + 20x + x2 = 0 + 3125 Combine like terms: -3125 + 3125 = 0 0 + 20x + x2 = 0 + 3125 20x + x2 = 0 + 3125 Combine like terms: 0 + 3125 = 3125 20x + x2 = 3125 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 3125 + 100 Reorder the terms: 100 + 20x + x2 = 3125 + 100 Combine like terms: 3125 + 100 = 3225 100 + 20x + x2 = 3225 Factor a perfect square on the left side: (x + 10)(x + 10) = 3225 Calculate the square root of the right side: 56.789083458 Break this problem into two subproblems by setting (x + 10) equal to 56.789083458 and -56.789083458.Subproblem 1
x + 10 = 56.789083458 Simplifying x + 10 = 56.789083458 Reorder the terms: 10 + x = 56.789083458 Solving 10 + x = 56.789083458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 56.789083458 + -10 Combine like terms: 10 + -10 = 0 0 + x = 56.789083458 + -10 x = 56.789083458 + -10 Combine like terms: 56.789083458 + -10 = 46.789083458 x = 46.789083458 Simplifying x = 46.789083458Subproblem 2
x + 10 = -56.789083458 Simplifying x + 10 = -56.789083458 Reorder the terms: 10 + x = -56.789083458 Solving 10 + x = -56.789083458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -56.789083458 + -10 Combine like terms: 10 + -10 = 0 0 + x = -56.789083458 + -10 x = -56.789083458 + -10 Combine like terms: -56.789083458 + -10 = -66.789083458 x = -66.789083458 Simplifying x = -66.789083458Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.789083458, -66.789083458}Solution
x = {46.789083458, -66.789083458}
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