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Simplifying 5x2 = x + 300 Reorder the terms: 5x2 = 300 + x Solving 5x2 = 300 + x Solving for variable 'x'. Reorder the terms: -300 + -1x + 5x2 = 300 + x + -300 + -1x Reorder the terms: -300 + -1x + 5x2 = 300 + -300 + x + -1x Combine like terms: 300 + -300 = 0 -300 + -1x + 5x2 = 0 + x + -1x -300 + -1x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -300 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -60 + -0.2x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -0.2x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -0.2x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -0.2x + x2 = 0 + 60 -0.2x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -0.2x + x2 = 60 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 = 60 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 60 + 0.01 Combine like terms: 60 + 0.01 = 60.01 0.01 + -0.2x + x2 = 60.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 60.01 Calculate the square root of the right side: 7.746612163 Break this problem into two subproblems by setting (x + -0.1) equal to 7.746612163 and -7.746612163.Subproblem 1
x + -0.1 = 7.746612163 Simplifying x + -0.1 = 7.746612163 Reorder the terms: -0.1 + x = 7.746612163 Solving -0.1 + x = 7.746612163 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 = 7.746612163 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 7.746612163 + 0.1 x = 7.746612163 + 0.1 Combine like terms: 7.746612163 + 0.1 = 7.846612163 x = 7.846612163 Simplifying x = 7.846612163Subproblem 2
x + -0.1 = -7.746612163 Simplifying x + -0.1 = -7.746612163 Reorder the terms: -0.1 + x = -7.746612163 Solving -0.1 + x = -7.746612163 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 = -7.746612163 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -7.746612163 + 0.1 x = -7.746612163 + 0.1 Combine like terms: -7.746612163 + 0.1 = -7.646612163 x = -7.646612163 Simplifying x = -7.646612163Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.846612163, -7.646612163}
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