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Simplifying 5x2 + -1x = 7 Reorder the terms: -1x + 5x2 = 7 Solving -1x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -1x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.2x + x2 = 0 + 1.4 -0.2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.2x + x2 = 1.4 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 1.4 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 1.4 + 0.01 Combine like terms: 1.4 + 0.01 = 1.41 0.01 + -0.2x + x2 = 1.41 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (x + -0.1) equal to 1.187434209 and -1.187434209.Subproblem 1
x + -0.1 = 1.187434209 Simplifying x + -0.1 = 1.187434209 Reorder the terms: -0.1 + x = 1.187434209 Solving -0.1 + x = 1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.187434209 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.187434209 + 0.1 x = 1.187434209 + 0.1 Combine like terms: 1.187434209 + 0.1 = 1.287434209 x = 1.287434209 Simplifying x = 1.287434209Subproblem 2
x + -0.1 = -1.187434209 Simplifying x + -0.1 = -1.187434209 Reorder the terms: -0.1 + x = -1.187434209 Solving -0.1 + x = -1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.187434209 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.187434209 + 0.1 x = -1.187434209 + 0.1 Combine like terms: -1.187434209 + 0.1 = -1.087434209 x = -1.087434209 Simplifying x = -1.087434209Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.287434209, -1.087434209}
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