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Simplifying x2 + 0.4x = 45 Reorder the terms: 0.4x + x2 = 45 Solving 0.4x + x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 0.4x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 0.4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 0.4x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 0.4x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 0.4x + x2 = 0 + 45 0.4x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 0.4x + x2 = 45 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 = 45 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 45 + 0.04 Combine like terms: 45 + 0.04 = 45.04 0.04 + 0.4x + x2 = 45.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 45.04 Calculate the square root of the right side: 6.711184694 Break this problem into two subproblems by setting (x + 0.2) equal to 6.711184694 and -6.711184694.Subproblem 1
x + 0.2 = 6.711184694 Simplifying x + 0.2 = 6.711184694 Reorder the terms: 0.2 + x = 6.711184694 Solving 0.2 + x = 6.711184694 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 = 6.711184694 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 6.711184694 + -0.2 x = 6.711184694 + -0.2 Combine like terms: 6.711184694 + -0.2 = 6.511184694 x = 6.511184694 Simplifying x = 6.511184694Subproblem 2
x + 0.2 = -6.711184694 Simplifying x + 0.2 = -6.711184694 Reorder the terms: 0.2 + x = -6.711184694 Solving 0.2 + x = -6.711184694 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 = -6.711184694 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -6.711184694 + -0.2 x = -6.711184694 + -0.2 Combine like terms: -6.711184694 + -0.2 = -6.911184694 x = -6.911184694 Simplifying x = -6.911184694Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.511184694, -6.911184694}
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