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Simplifying 10x + -10x2 = 0.9 Solving 10x + -10x2 = 0.9 Solving for variable 'x'. Reorder the terms: -0.9 + 10x + -10x2 = 0.9 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 -0.9 + 10x + -10x2 = 0.0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.09 + -1x + x2 = 0.0 Move the constant term to the right: Add '-0.09' to each side of the equation. 0.09 + -1x + -0.09 + x2 = 0.0 + -0.09 Reorder the terms: 0.09 + -0.09 + -1x + x2 = 0.0 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + -1x + x2 = 0.0 + -0.09 -1x + x2 = 0.0 + -0.09 Combine like terms: 0.0 + -0.09 = -0.09 -1x + x2 = -0.09 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.09 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.09 + 0.25 Combine like terms: -0.09 + 0.25 = 0.16 0.25 + -1x + x2 = 0.16 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -0.5) equal to 0.4 and -0.4.Subproblem 1
x + -0.5 = 0.4 Simplifying x + -0.5 = 0.4 Reorder the terms: -0.5 + x = 0.4 Solving -0.5 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.4 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.4 + 0.5 x = 0.4 + 0.5 Combine like terms: 0.4 + 0.5 = 0.9 x = 0.9 Simplifying x = 0.9Subproblem 2
x + -0.5 = -0.4 Simplifying x + -0.5 = -0.4 Reorder the terms: -0.5 + x = -0.4 Solving -0.5 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.4 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.4 + 0.5 x = -0.4 + 0.5 Combine like terms: -0.4 + 0.5 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9, 0.1}
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