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Simplifying (10x)(10x) + -6 = 9x Remove parenthesis around (10x) 10x(10x) + -6 = 9x Remove parenthesis around (10x) 10x * 10x + -6 = 9x Reorder the terms for easier multiplication: 10 * 10x * x + -6 = 9x Multiply 10 * 10 100x * x + -6 = 9x Multiply x * x 100x2 + -6 = 9x Reorder the terms: -6 + 100x2 = 9x Solving -6 + 100x2 = 9x Solving for variable 'x'. Reorder the terms: -6 + -9x + 100x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -6 + -9x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.06 + -0.09x + x2 = 0.00 Move the constant term to the right: Add '0.06' to each side of the equation. -0.06 + -0.09x + 0.06 + x2 = 0.00 + 0.06 Reorder the terms: -0.06 + 0.06 + -0.09x + x2 = 0.00 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + -0.09x + x2 = 0.00 + 0.06 -0.09x + x2 = 0.00 + 0.06 Combine like terms: 0.00 + 0.06 = 0.06 -0.09x + x2 = 0.06 The x term is -0.09x. Take half its coefficient (-0.045). Square it (0.002025) and add it to both sides. Add '0.002025' to each side of the equation. -0.09x + 0.002025 + x2 = 0.06 + 0.002025 Reorder the terms: 0.002025 + -0.09x + x2 = 0.06 + 0.002025 Combine like terms: 0.06 + 0.002025 = 0.062025 0.002025 + -0.09x + x2 = 0.062025 Factor a perfect square on the left side: (x + -0.045)(x + -0.045) = 0.062025 Calculate the square root of the right side: 0.249048188 Break this problem into two subproblems by setting (x + -0.045) equal to 0.249048188 and -0.249048188.Subproblem 1
x + -0.045 = 0.249048188 Simplifying x + -0.045 = 0.249048188 Reorder the terms: -0.045 + x = 0.249048188 Solving -0.045 + x = 0.249048188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.045' to each side of the equation. -0.045 + 0.045 + x = 0.249048188 + 0.045 Combine like terms: -0.045 + 0.045 = 0.000 0.000 + x = 0.249048188 + 0.045 x = 0.249048188 + 0.045 Combine like terms: 0.249048188 + 0.045 = 0.294048188 x = 0.294048188 Simplifying x = 0.294048188Subproblem 2
x + -0.045 = -0.249048188 Simplifying x + -0.045 = -0.249048188 Reorder the terms: -0.045 + x = -0.249048188 Solving -0.045 + x = -0.249048188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.045' to each side of the equation. -0.045 + 0.045 + x = -0.249048188 + 0.045 Combine like terms: -0.045 + 0.045 = 0.000 0.000 + x = -0.249048188 + 0.045 x = -0.249048188 + 0.045 Combine like terms: -0.249048188 + 0.045 = -0.204048188 x = -0.204048188 Simplifying x = -0.204048188Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.294048188, -0.204048188}
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