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Simplifying 7 = (0.1 + -1x)(0.1 + -1x) Multiply (0.1 + -1x) * (0.1 + -1x) 7 = (0.1(0.1 + -1x) + -1x * (0.1 + -1x)) 7 = ((0.1 * 0.1 + -1x * 0.1) + -1x * (0.1 + -1x)) 7 = ((0.01 + -0.1x) + -1x * (0.1 + -1x)) 7 = (0.01 + -0.1x + (0.1 * -1x + -1x * -1x)) 7 = (0.01 + -0.1x + (-0.1x + 1x2)) Combine like terms: -0.1x + -0.1x = -0.2x 7 = (0.01 + -0.2x + 1x2) Solving 7 = 0.01 + -0.2x + 1x2 Solving for variable 'x'. Combine like terms: 7 + -0.01 = 6.99 6.99 + 0.2x + -1x2 = 0.01 + -0.2x + 1x2 + -0.01 + 0.2x + -1x2 Reorder the terms: 6.99 + 0.2x + -1x2 = 0.01 + -0.01 + -0.2x + 0.2x + 1x2 + -1x2 Combine like terms: 0.01 + -0.01 = 0.00 6.99 + 0.2x + -1x2 = 0.00 + -0.2x + 0.2x + 1x2 + -1x2 6.99 + 0.2x + -1x2 = -0.2x + 0.2x + 1x2 + -1x2 Combine like terms: -0.2x + 0.2x = 0.0 6.99 + 0.2x + -1x2 = 0.0 + 1x2 + -1x2 6.99 + 0.2x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 6.99 + 0.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6.99 + -0.2x + x2 = 0 Move the constant term to the right: Add '6.99' to each side of the equation. -6.99 + -0.2x + 6.99 + x2 = 0 + 6.99 Reorder the terms: -6.99 + 6.99 + -0.2x + x2 = 0 + 6.99 Combine like terms: -6.99 + 6.99 = 0.00 0.00 + -0.2x + x2 = 0 + 6.99 -0.2x + x2 = 0 + 6.99 Combine like terms: 0 + 6.99 = 6.99 -0.2x + x2 = 6.99 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 6.99 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 6.99 + 0.01 Combine like terms: 6.99 + 0.01 = 7 0.01 + -0.2x + x2 = 7 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -0.1) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -0.1 = 2.645751311 Simplifying x + -0.1 = 2.645751311 Reorder the terms: -0.1 + x = 2.645751311 Solving -0.1 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 2.645751311 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 2.645751311 + 0.1 x = 2.645751311 + 0.1 Combine like terms: 2.645751311 + 0.1 = 2.745751311 x = 2.745751311 Simplifying x = 2.745751311Subproblem 2
x + -0.1 = -2.645751311 Simplifying x + -0.1 = -2.645751311 Reorder the terms: -0.1 + x = -2.645751311 Solving -0.1 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -2.645751311 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -2.645751311 + 0.1 x = -2.645751311 + 0.1 Combine like terms: -2.645751311 + 0.1 = -2.545751311 x = -2.545751311 Simplifying x = -2.545751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.745751311, -2.545751311}
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