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Simplifying -4.9x2 + 9x + 1.2 = 0 Reorder the terms: 1.2 + 9x + -4.9x2 = 0 Solving 1.2 + 9x + -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'. -0.2448979592 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '0.2448979592' to each side of the equation. -0.2448979592 + -1.836734694x + 0.2448979592 + x2 = 0 + 0.2448979592 Reorder the terms: -0.2448979592 + 0.2448979592 + -1.836734694x + x2 = 0 + 0.2448979592 Combine like terms: -0.2448979592 + 0.2448979592 = 0.0000000000 0.0000000000 + -1.836734694x + x2 = 0 + 0.2448979592 -1.836734694x + x2 = 0 + 0.2448979592 Combine like terms: 0 + 0.2448979592 = 0.2448979592 -1.836734694x + x2 = 0.2448979592 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 0.2448979592 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 0.2448979592 + 0.8433985840 Combine like terms: 0.2448979592 + 0.8433985840 = 1.0882965432 0.8433985840 + -1.836734694x + x2 = 1.0882965432 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 1.0882965432 Calculate the square root of the right side: 1.043214524 Break this problem into two subproblems by setting (x + -0.918367347) equal to 1.043214524 and -1.043214524.Subproblem 1
x + -0.918367347 = 1.043214524 Simplifying x + -0.918367347 = 1.043214524 Reorder the terms: -0.918367347 + x = 1.043214524 Solving -0.918367347 + x = 1.043214524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 1.043214524 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 1.043214524 + 0.918367347 x = 1.043214524 + 0.918367347 Combine like terms: 1.043214524 + 0.918367347 = 1.961581871 x = 1.961581871 Simplifying x = 1.961581871Subproblem 2
x + -0.918367347 = -1.043214524 Simplifying x + -0.918367347 = -1.043214524 Reorder the terms: -0.918367347 + x = -1.043214524 Solving -0.918367347 + x = -1.043214524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -1.043214524 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -1.043214524 + 0.918367347 x = -1.043214524 + 0.918367347 Combine like terms: -1.043214524 + 0.918367347 = -0.124847177 x = -0.124847177 Simplifying x = -0.124847177Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.961581871, -0.124847177}
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