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Simplifying 0.034 + 0.17x = x2 Solving 0.034 + 0.17x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.034 + 0.17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.034 + -0.17x + x2 = 0 Move the constant term to the right: Add '0.034' to each side of the equation. -0.034 + -0.17x + 0.034 + x2 = 0 + 0.034 Reorder the terms: -0.034 + 0.034 + -0.17x + x2 = 0 + 0.034 Combine like terms: -0.034 + 0.034 = 0.000 0.000 + -0.17x + x2 = 0 + 0.034 -0.17x + x2 = 0 + 0.034 Combine like terms: 0 + 0.034 = 0.034 -0.17x + x2 = 0.034 The x term is -0.17x. Take half its coefficient (-0.085). Square it (0.007225) and add it to both sides. Add '0.007225' to each side of the equation. -0.17x + 0.007225 + x2 = 0.034 + 0.007225 Reorder the terms: 0.007225 + -0.17x + x2 = 0.034 + 0.007225 Combine like terms: 0.034 + 0.007225 = 0.041225 0.007225 + -0.17x + x2 = 0.041225 Factor a perfect square on the left side: (x + -0.085)(x + -0.085) = 0.041225 Calculate the square root of the right side: 0.203039405 Break this problem into two subproblems by setting (x + -0.085) equal to 0.203039405 and -0.203039405.Subproblem 1
x + -0.085 = 0.203039405 Simplifying x + -0.085 = 0.203039405 Reorder the terms: -0.085 + x = 0.203039405 Solving -0.085 + x = 0.203039405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.085' to each side of the equation. -0.085 + 0.085 + x = 0.203039405 + 0.085 Combine like terms: -0.085 + 0.085 = 0.000 0.000 + x = 0.203039405 + 0.085 x = 0.203039405 + 0.085 Combine like terms: 0.203039405 + 0.085 = 0.288039405 x = 0.288039405 Simplifying x = 0.288039405Subproblem 2
x + -0.085 = -0.203039405 Simplifying x + -0.085 = -0.203039405 Reorder the terms: -0.085 + x = -0.203039405 Solving -0.085 + x = -0.203039405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.085' to each side of the equation. -0.085 + 0.085 + x = -0.203039405 + 0.085 Combine like terms: -0.085 + 0.085 = 0.000 0.000 + x = -0.203039405 + 0.085 x = -0.203039405 + 0.085 Combine like terms: -0.203039405 + 0.085 = -0.118039405 x = -0.118039405 Simplifying x = -0.118039405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288039405, -0.118039405}
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