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Simplifying 10x2 + 7x + -5 = 0 Reorder the terms: -5 + 7x + 10x2 = 0 Solving -5 + 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'. -0.5 + 0.7x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.7x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.7x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.7x + x2 = 0 + 0.5 0.7x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.7x + x2 = 0.5 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 = 0.5 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.5 + 0.1225 Combine like terms: 0.5 + 0.1225 = 0.6225 0.1225 + 0.7x + x2 = 0.6225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.6225 Calculate the square root of the right side: 0.788986692 Break this problem into two subproblems by setting (x + 0.35) equal to 0.788986692 and -0.788986692.Subproblem 1
x + 0.35 = 0.788986692 Simplifying x + 0.35 = 0.788986692 Reorder the terms: 0.35 + x = 0.788986692 Solving 0.35 + x = 0.788986692 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 = 0.788986692 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.788986692 + -0.35 x = 0.788986692 + -0.35 Combine like terms: 0.788986692 + -0.35 = 0.438986692 x = 0.438986692 Simplifying x = 0.438986692Subproblem 2
x + 0.35 = -0.788986692 Simplifying x + 0.35 = -0.788986692 Reorder the terms: 0.35 + x = -0.788986692 Solving 0.35 + x = -0.788986692 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 = -0.788986692 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.788986692 + -0.35 x = -0.788986692 + -0.35 Combine like terms: -0.788986692 + -0.35 = -1.138986692 x = -1.138986692 Simplifying x = -1.138986692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438986692, -1.138986692}
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