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Simplifying 10x2 + -1x + -3 = 3 Reorder the terms: -3 + -1x + 10x2 = 3 Solving -3 + -1x + 10x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -3 + -1x + 10x2 = 3 + -3 Combine like terms: -3 + -3 = -6 -6 + -1x + 10x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -6 + -1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -0.1x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.1x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.1x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.1x + x2 = 0 + 0.6 -0.1x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.1x + x2 = 0.6 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 0.6 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.6 + 0.0025 Combine like terms: 0.6 + 0.0025 = 0.6025 0.0025 + -0.1x + x2 = 0.6025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + -0.05) equal to 0.776208735 and -0.776208735.Subproblem 1
x + -0.05 = 0.776208735 Simplifying x + -0.05 = 0.776208735 Reorder the terms: -0.05 + x = 0.776208735 Solving -0.05 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 0.776208735 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.776208735 + 0.05 x = 0.776208735 + 0.05 Combine like terms: 0.776208735 + 0.05 = 0.826208735 x = 0.826208735 Simplifying x = 0.826208735Subproblem 2
x + -0.05 = -0.776208735 Simplifying x + -0.05 = -0.776208735 Reorder the terms: -0.05 + x = -0.776208735 Solving -0.05 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -0.776208735 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.776208735 + 0.05 x = -0.776208735 + 0.05 Combine like terms: -0.776208735 + 0.05 = -0.726208735 x = -0.726208735 Simplifying x = -0.726208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.826208735, -0.726208735}
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