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Simplifying -1x2 + -0.7x + 0.1988 = 0 Reorder the terms: 0.1988 + -0.7x + -1x2 = 0 Solving 0.1988 + -0.7x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.1988 + 0.7x + x2 = 0 Move the constant term to the right: Add '0.1988' to each side of the equation. -0.1988 + 0.7x + 0.1988 + x2 = 0 + 0.1988 Reorder the terms: -0.1988 + 0.1988 + 0.7x + x2 = 0 + 0.1988 Combine like terms: -0.1988 + 0.1988 = 0.0000 0.0000 + 0.7x + x2 = 0 + 0.1988 0.7x + x2 = 0 + 0.1988 Combine like terms: 0 + 0.1988 = 0.1988 0.7x + x2 = 0.1988 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 0.1988 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.1988 + 0.1225 Combine like terms: 0.1988 + 0.1225 = 0.3213 0.1225 + 0.7x + x2 = 0.3213 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.3213 Calculate the square root of the right side: 0.566833309 Break this problem into two subproblems by setting (x + 0.35) equal to 0.566833309 and -0.566833309.Subproblem 1
x + 0.35 = 0.566833309 Simplifying x + 0.35 = 0.566833309 Reorder the terms: 0.35 + x = 0.566833309 Solving 0.35 + x = 0.566833309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.566833309 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.566833309 + -0.35 x = 0.566833309 + -0.35 Combine like terms: 0.566833309 + -0.35 = 0.216833309 x = 0.216833309 Simplifying x = 0.216833309Subproblem 2
x + 0.35 = -0.566833309 Simplifying x + 0.35 = -0.566833309 Reorder the terms: 0.35 + x = -0.566833309 Solving 0.35 + x = -0.566833309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.566833309 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.566833309 + -0.35 x = -0.566833309 + -0.35 Combine like terms: -0.566833309 + -0.35 = -0.916833309 x = -0.916833309 Simplifying x = -0.916833309Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.216833309, -0.916833309}
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