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Simplifying 0.7x2 = 1.4x + 0.07 Reorder the terms: 0.7x2 = 0.07 + 1.4x Solving 0.7x2 = 0.07 + 1.4x Solving for variable 'x'. Reorder the terms: -0.07 + -1.4x + 0.7x2 = 0.07 + 1.4x + -0.07 + -1.4x Reorder the terms: -0.07 + -1.4x + 0.7x2 = 0.07 + -0.07 + 1.4x + -1.4x Combine like terms: 0.07 + -0.07 = 0.00 -0.07 + -1.4x + 0.7x2 = 0.00 + 1.4x + -1.4x -0.07 + -1.4x + 0.7x2 = 1.4x + -1.4x Combine like terms: 1.4x + -1.4x = 0.0 -0.07 + -1.4x + 0.7x2 = 0.0 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -0.1 + -2x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -2x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -2x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -2x + x2 = 0 + 0.1 -2x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -2x + x2 = 0.1 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 = 0.1 + 1 Reorder the terms: 1 + -2x + x2 = 0.1 + 1 Combine like terms: 0.1 + 1 = 1.1 1 + -2x + x2 = 1.1 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.1 Calculate the square root of the right side: 1.048808848 Break this problem into two subproblems by setting (x + -1) equal to 1.048808848 and -1.048808848.Subproblem 1
x + -1 = 1.048808848 Simplifying x + -1 = 1.048808848 Reorder the terms: -1 + x = 1.048808848 Solving -1 + x = 1.048808848 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 = 1.048808848 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.048808848 + 1 x = 1.048808848 + 1 Combine like terms: 1.048808848 + 1 = 2.048808848 x = 2.048808848 Simplifying x = 2.048808848Subproblem 2
x + -1 = -1.048808848 Simplifying x + -1 = -1.048808848 Reorder the terms: -1 + x = -1.048808848 Solving -1 + x = -1.048808848 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 = -1.048808848 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.048808848 + 1 x = -1.048808848 + 1 Combine like terms: -1.048808848 + 1 = -0.048808848 x = -0.048808848 Simplifying x = -0.048808848Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.048808848, -0.048808848}
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