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Simplifying 9x + 3 = 10x2 Reorder the terms: 3 + 9x = 10x2 Solving 3 + 9x = 10x2 Solving for variable 'x'. Combine like terms: 10x2 + -10x2 = 0 3 + 9x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + -0.9x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.9x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.9x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.9x + x2 = 0 + 0.3 -0.9x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -0.9x + x2 = 0.3 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = 0.3 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 0.3 + 0.2025 Combine like terms: 0.3 + 0.2025 = 0.5025 0.2025 + -0.9x + x2 = 0.5025 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (x + -0.45) equal to 0.708872344 and -0.708872344.Subproblem 1
x + -0.45 = 0.708872344 Simplifying x + -0.45 = 0.708872344 Reorder the terms: -0.45 + x = 0.708872344 Solving -0.45 + x = 0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.708872344 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.708872344 + 0.45 x = 0.708872344 + 0.45 Combine like terms: 0.708872344 + 0.45 = 1.158872344 x = 1.158872344 Simplifying x = 1.158872344Subproblem 2
x + -0.45 = -0.708872344 Simplifying x + -0.45 = -0.708872344 Reorder the terms: -0.45 + x = -0.708872344 Solving -0.45 + x = -0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.708872344 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.708872344 + 0.45 x = -0.708872344 + 0.45 Combine like terms: -0.708872344 + 0.45 = -0.258872344 x = -0.258872344 Simplifying x = -0.258872344Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.158872344, -0.258872344}
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