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Simplifying -10x2 + 7x + 7 = 0 Reorder the terms: 7 + 7x + -10x2 = 0 Solving 7 + 7x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.7 + -0.7x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -0.7x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -0.7x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -0.7x + x2 = 0 + 0.7 -0.7x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -0.7x + x2 = 0.7 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 = 0.7 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 0.7 + 0.1225 Combine like terms: 0.7 + 0.1225 = 0.8225 0.1225 + -0.7x + x2 = 0.8225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.8225 Calculate the square root of the right side: 0.906917857 Break this problem into two subproblems by setting (x + -0.35) equal to 0.906917857 and -0.906917857.Subproblem 1
x + -0.35 = 0.906917857 Simplifying x + -0.35 = 0.906917857 Reorder the terms: -0.35 + x = 0.906917857 Solving -0.35 + x = 0.906917857 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 = 0.906917857 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.906917857 + 0.35 x = 0.906917857 + 0.35 Combine like terms: 0.906917857 + 0.35 = 1.256917857 x = 1.256917857 Simplifying x = 1.256917857Subproblem 2
x + -0.35 = -0.906917857 Simplifying x + -0.35 = -0.906917857 Reorder the terms: -0.35 + x = -0.906917857 Solving -0.35 + x = -0.906917857 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 = -0.906917857 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -0.906917857 + 0.35 x = -0.906917857 + 0.35 Combine like terms: -0.906917857 + 0.35 = -0.556917857 x = -0.556917857 Simplifying x = -0.556917857Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.256917857, -0.556917857}
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