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Simplifying -4.9x2 + 6.5x + 10 = 0 Reorder the terms: 10 + 6.5x + -4.9x2 = 0 Solving 10 + 6.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.040816327 + -1.326530612x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -1.326530612x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -1.326530612x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -1.326530612x + x2 = 0 + 2.040816327 -1.326530612x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -1.326530612x + x2 = 2.040816327 The x term is -1.326530612x. Take half its coefficient (-0.663265306). Square it (0.4399208661) and add it to both sides. Add '0.4399208661' to each side of the equation. -1.326530612x + 0.4399208661 + x2 = 2.040816327 + 0.4399208661 Reorder the terms: 0.4399208661 + -1.326530612x + x2 = 2.040816327 + 0.4399208661 Combine like terms: 2.040816327 + 0.4399208661 = 2.4807371931 0.4399208661 + -1.326530612x + x2 = 2.4807371931 Factor a perfect square on the left side: (x + -0.663265306)(x + -0.663265306) = 2.4807371931 Calculate the square root of the right side: 1.575035616 Break this problem into two subproblems by setting (x + -0.663265306) equal to 1.575035616 and -1.575035616.Subproblem 1
x + -0.663265306 = 1.575035616 Simplifying x + -0.663265306 = 1.575035616 Reorder the terms: -0.663265306 + x = 1.575035616 Solving -0.663265306 + x = 1.575035616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.663265306' to each side of the equation. -0.663265306 + 0.663265306 + x = 1.575035616 + 0.663265306 Combine like terms: -0.663265306 + 0.663265306 = 0.000000000 0.000000000 + x = 1.575035616 + 0.663265306 x = 1.575035616 + 0.663265306 Combine like terms: 1.575035616 + 0.663265306 = 2.238300922 x = 2.238300922 Simplifying x = 2.238300922Subproblem 2
x + -0.663265306 = -1.575035616 Simplifying x + -0.663265306 = -1.575035616 Reorder the terms: -0.663265306 + x = -1.575035616 Solving -0.663265306 + x = -1.575035616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.663265306' to each side of the equation. -0.663265306 + 0.663265306 + x = -1.575035616 + 0.663265306 Combine like terms: -0.663265306 + 0.663265306 = 0.000000000 0.000000000 + x = -1.575035616 + 0.663265306 x = -1.575035616 + 0.663265306 Combine like terms: -1.575035616 + 0.663265306 = -0.91177031 x = -0.91177031 Simplifying x = -0.91177031Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.238300922, -0.91177031}
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