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Simplifying 10x(5x) + -3 = 20x + 15 Remove parenthesis around (5x) 10x * 5x + -3 = 20x + 15 Reorder the terms for easier multiplication: 10 * 5x * x + -3 = 20x + 15 Multiply 10 * 5 50x * x + -3 = 20x + 15 Multiply x * x 50x2 + -3 = 20x + 15 Reorder the terms: -3 + 50x2 = 20x + 15 Reorder the terms: -3 + 50x2 = 15 + 20x Solving -3 + 50x2 = 15 + 20x Solving for variable 'x'. Reorder the terms: -3 + -15 + -20x + 50x2 = 15 + 20x + -15 + -20x Combine like terms: -3 + -15 = -18 -18 + -20x + 50x2 = 15 + 20x + -15 + -20x Reorder the terms: -18 + -20x + 50x2 = 15 + -15 + 20x + -20x Combine like terms: 15 + -15 = 0 -18 + -20x + 50x2 = 0 + 20x + -20x -18 + -20x + 50x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -18 + -20x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -10x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -10x + 25x2)' equal to zero and attempt to solve: Simplifying -9 + -10x + 25x2 = 0 Solving -9 + -10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.36 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + -0.4x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + -0.4x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + -0.4x + x2 = 0 + 0.36 -0.4x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 -0.4x + x2 = 0.36 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.36 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.36 + 0.04 Combine like terms: 0.36 + 0.04 = 0.4 0.04 + -0.4x + x2 = 0.4 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + -0.2) equal to 0.632455532 and -0.632455532.Subproblem 1
x + -0.2 = 0.632455532 Simplifying x + -0.2 = 0.632455532 Reorder the terms: -0.2 + x = 0.632455532 Solving -0.2 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.632455532 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.632455532 + 0.2 x = 0.632455532 + 0.2 Combine like terms: 0.632455532 + 0.2 = 0.832455532 x = 0.832455532 Simplifying x = 0.832455532Subproblem 2
x + -0.2 = -0.632455532 Simplifying x + -0.2 = -0.632455532 Reorder the terms: -0.2 + x = -0.632455532 Solving -0.2 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.632455532 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.632455532 + 0.2 x = -0.632455532 + 0.2 Combine like terms: -0.632455532 + 0.2 = -0.432455532 x = -0.432455532 Simplifying x = -0.432455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.832455532, -0.432455532}Solution
x = {0.832455532, -0.432455532}
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