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Simplifying 4 = 40 + 2x + -5x2 Solving 4 = 40 + 2x + -5x2 Solving for variable 'x'. Combine like terms: 4 + -40 = -36 -36 + -2x + 5x2 = 40 + 2x + -5x2 + -40 + -2x + 5x2 Reorder the terms: -36 + -2x + 5x2 = 40 + -40 + 2x + -2x + -5x2 + 5x2 Combine like terms: 40 + -40 = 0 -36 + -2x + 5x2 = 0 + 2x + -2x + -5x2 + 5x2 -36 + -2x + 5x2 = 2x + -2x + -5x2 + 5x2 Combine like terms: 2x + -2x = 0 -36 + -2x + 5x2 = 0 + -5x2 + 5x2 -36 + -2x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -36 + -2x + 5x2 = 0 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 = 2.890724809 x = 2.890724809 Simplifying x = 2.890724809Subproblem 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 = -2.490724809 x = -2.490724809 Simplifying x = -2.490724809Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.890724809, -2.490724809}
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