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Simplifying 36 + -2x + -5x2 = 0 Solving 36 + -2x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -7.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 0.4x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 0.4x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 0.4x + x2 = 0 + 7.2 0.4x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 0.4x + x2 = 7.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 7.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 7.2 + 0.04 Combine like terms: 7.2 + 0.04 = 7.24 0.04 + 0.4x + x2 = 7.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 7.24 Calculate the square root of the right side: 2.690724809 Break this problem into two subproblems by setting (x + 0.2) equal to 2.690724809 and -2.690724809.Subproblem 1
x + 0.2 = 2.690724809 Simplifying x + 0.2 = 2.690724809 Reorder the terms: 0.2 + x = 2.690724809 Solving 0.2 + x = 2.690724809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 2.690724809 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.690724809 + -0.2 x = 2.690724809 + -0.2 Combine like terms: 2.690724809 + -0.2 = 2.490724809 x = 2.490724809 Simplifying x = 2.490724809Subproblem 2
x + 0.2 = -2.690724809 Simplifying x + 0.2 = -2.690724809 Reorder the terms: 0.2 + x = -2.690724809 Solving 0.2 + x = -2.690724809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -2.690724809 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.690724809 + -0.2 x = -2.690724809 + -0.2 Combine like terms: -2.690724809 + -0.2 = -2.890724809 x = -2.890724809 Simplifying x = -2.890724809Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.490724809, -2.890724809}
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