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Simplifying x2 + 2x + 1 = 1.56 Reorder the terms: 1 + 2x + x2 = 1.56 Solving 1 + 2x + x2 = 1.56 Solving for variable 'x'. Reorder the terms: 1 + -1.56 + 2x + x2 = 1.56 + -1.56 Combine like terms: 1 + -1.56 = -0.56 -0.56 + 2x + x2 = 1.56 + -1.56 Combine like terms: 1.56 + -1.56 = 0.00 -0.56 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + 2x + 0.56 + x2 = 0.00 + 0.56 Reorder the terms: -0.56 + 0.56 + 2x + x2 = 0.00 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + 2x + x2 = 0.00 + 0.56 2x + x2 = 0.00 + 0.56 Combine like terms: 0.00 + 0.56 = 0.56 2x + x2 = 0.56 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.56 + 1 Reorder the terms: 1 + 2x + x2 = 0.56 + 1 Combine like terms: 0.56 + 1 = 1.56 1 + 2x + x2 = 1.56 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (x + 1) equal to 1.2489996 and -1.2489996.Subproblem 1
x + 1 = 1.2489996 Simplifying x + 1 = 1.2489996 Reorder the terms: 1 + x = 1.2489996 Solving 1 + x = 1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.2489996 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.2489996 + -1 x = 1.2489996 + -1 Combine like terms: 1.2489996 + -1 = 0.2489996 x = 0.2489996 Simplifying x = 0.2489996Subproblem 2
x + 1 = -1.2489996 Simplifying x + 1 = -1.2489996 Reorder the terms: 1 + x = -1.2489996 Solving 1 + x = -1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.2489996 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.2489996 + -1 x = -1.2489996 + -1 Combine like terms: -1.2489996 + -1 = -2.2489996 x = -2.2489996 Simplifying x = -2.2489996Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2489996, -2.2489996}
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