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Simplifying 0.7 = 2x + -1x2 Solving 0.7 = 2x + -1x2 Solving for variable 'x'. Reorder the terms: 0.7 + -2x + x2 = 2x + -2x + -1x2 + x2 Combine like terms: 2x + -2x = 0 0.7 + -2x + x2 = 0 + -1x2 + x2 0.7 + -2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 0.7 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -2x + -0.7 + x2 = 0 + -0.7 Reorder the terms: 0.7 + -0.7 + -2x + x2 = 0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -2x + x2 = 0 + -0.7 -2x + x2 = 0 + -0.7 Combine like terms: 0 + -0.7 = -0.7 -2x + x2 = -0.7 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 = -0.7 + 1 Reorder the terms: 1 + -2x + x2 = -0.7 + 1 Combine like terms: -0.7 + 1 = 0.3 1 + -2x + x2 = 0.3 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.3 Calculate the square root of the right side: 0.547722558 Break this problem into two subproblems by setting (x + -1) equal to 0.547722558 and -0.547722558.Subproblem 1
x + -1 = 0.547722558 Simplifying x + -1 = 0.547722558 Reorder the terms: -1 + x = 0.547722558 Solving -1 + x = 0.547722558 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 = 0.547722558 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.547722558 + 1 x = 0.547722558 + 1 Combine like terms: 0.547722558 + 1 = 1.547722558 x = 1.547722558 Simplifying x = 1.547722558Subproblem 2
x + -1 = -0.547722558 Simplifying x + -1 = -0.547722558 Reorder the terms: -1 + x = -0.547722558 Solving -1 + x = -0.547722558 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 = -0.547722558 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.547722558 + 1 x = -0.547722558 + 1 Combine like terms: -0.547722558 + 1 = 0.452277442 x = 0.452277442 Simplifying x = 0.452277442Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.547722558, 0.452277442}
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