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Simplifying 4.59x2 + -9.76x + 2.98 = 0 Reorder the terms: 2.98 + -9.76x + 4.59x2 = 0 Solving 2.98 + -9.76x + 4.59x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.59 the coefficient of the squared term: Divide each side by '4.59'. 0.6492374728 + -2.126361656x + x2 = 0 Move the constant term to the right: Add '-0.6492374728' to each side of the equation. 0.6492374728 + -2.126361656x + -0.6492374728 + x2 = 0 + -0.6492374728 Reorder the terms: 0.6492374728 + -0.6492374728 + -2.126361656x + x2 = 0 + -0.6492374728 Combine like terms: 0.6492374728 + -0.6492374728 = 0.0000000000 0.0000000000 + -2.126361656x + x2 = 0 + -0.6492374728 -2.126361656x + x2 = 0 + -0.6492374728 Combine like terms: 0 + -0.6492374728 = -0.6492374728 -2.126361656x + x2 = -0.6492374728 The x term is -2.126361656x. Take half its coefficient (-1.063180828). Square it (1.130353473) and add it to both sides. Add '1.130353473' to each side of the equation. -2.126361656x + 1.130353473 + x2 = -0.6492374728 + 1.130353473 Reorder the terms: 1.130353473 + -2.126361656x + x2 = -0.6492374728 + 1.130353473 Combine like terms: -0.6492374728 + 1.130353473 = 0.4811160002 1.130353473 + -2.126361656x + x2 = 0.4811160002 Factor a perfect square on the left side: (x + -1.063180828)(x + -1.063180828) = 0.4811160002 Calculate the square root of the right side: 0.693625259 Break this problem into two subproblems by setting (x + -1.063180828) equal to 0.693625259 and -0.693625259.Subproblem 1
x + -1.063180828 = 0.693625259 Simplifying x + -1.063180828 = 0.693625259 Reorder the terms: -1.063180828 + x = 0.693625259 Solving -1.063180828 + x = 0.693625259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.063180828' to each side of the equation. -1.063180828 + 1.063180828 + x = 0.693625259 + 1.063180828 Combine like terms: -1.063180828 + 1.063180828 = 0.000000000 0.000000000 + x = 0.693625259 + 1.063180828 x = 0.693625259 + 1.063180828 Combine like terms: 0.693625259 + 1.063180828 = 1.756806087 x = 1.756806087 Simplifying x = 1.756806087Subproblem 2
x + -1.063180828 = -0.693625259 Simplifying x + -1.063180828 = -0.693625259 Reorder the terms: -1.063180828 + x = -0.693625259 Solving -1.063180828 + x = -0.693625259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.063180828' to each side of the equation. -1.063180828 + 1.063180828 + x = -0.693625259 + 1.063180828 Combine like terms: -1.063180828 + 1.063180828 = 0.000000000 0.000000000 + x = -0.693625259 + 1.063180828 x = -0.693625259 + 1.063180828 Combine like terms: -0.693625259 + 1.063180828 = 0.369555569 x = 0.369555569 Simplifying x = 0.369555569Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.756806087, 0.369555569}
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