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Simplifying x2 + 0.6x = 0.91 Reorder the terms: 0.6x + x2 = 0.91 Solving 0.6x + x2 = 0.91 Solving for variable 'x'. Reorder the terms: -0.91 + 0.6x + x2 = 0.91 + -0.91 Combine like terms: 0.91 + -0.91 = 0.00 -0.91 + 0.6x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.91' to each side of the equation. -0.91 + 0.6x + 0.91 + x2 = 0.00 + 0.91 Reorder the terms: -0.91 + 0.91 + 0.6x + x2 = 0.00 + 0.91 Combine like terms: -0.91 + 0.91 = 0.00 0.00 + 0.6x + x2 = 0.00 + 0.91 0.6x + x2 = 0.00 + 0.91 Combine like terms: 0.00 + 0.91 = 0.91 0.6x + x2 = 0.91 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.91 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.91 + 0.09 Combine like terms: 0.91 + 0.09 = 1 0.09 + 0.6x + x2 = 1 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 0.3) equal to 1 and -1.Subproblem 1
x + 0.3 = 1 Simplifying x + 0.3 = 1 Reorder the terms: 0.3 + x = 1 Solving 0.3 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1 + -0.3 x = 1 + -0.3 Combine like terms: 1 + -0.3 = 0.7 x = 0.7 Simplifying x = 0.7Subproblem 2
x + 0.3 = -1 Simplifying x + 0.3 = -1 Reorder the terms: 0.3 + x = -1 Solving 0.3 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1 + -0.3 x = -1 + -0.3 Combine like terms: -1 + -0.3 = -1.3 x = -1.3 Simplifying x = -1.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7, -1.3}
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