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Simplifying 4.9x2 + 2.74x = 10 Reorder the terms: 2.74x + 4.9x2 = 10 Solving 2.74x + 4.9x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 2.74x + 4.9x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 2.74x + 4.9x2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.040816327 + 0.5591836735x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 0.5591836735x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 0.5591836735x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 0.5591836735x + x2 = 0 + 2.040816327 0.5591836735x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 0.5591836735x + x2 = 2.040816327 The x term is 0.5591836735x. Take half its coefficient (0.2795918368). Square it (0.07817159521) and add it to both sides. Add '0.07817159521' to each side of the equation. 0.5591836735x + 0.07817159521 + x2 = 2.040816327 + 0.07817159521 Reorder the terms: 0.07817159521 + 0.5591836735x + x2 = 2.040816327 + 0.07817159521 Combine like terms: 2.040816327 + 0.07817159521 = 2.11898792221 0.07817159521 + 0.5591836735x + x2 = 2.11898792221 Factor a perfect square on the left side: (x + 0.2795918368)(x + 0.2795918368) = 2.11898792221 Calculate the square root of the right side: 1.455674387 Break this problem into two subproblems by setting (x + 0.2795918368) equal to 1.455674387 and -1.455674387.Subproblem 1
x + 0.2795918368 = 1.455674387 Simplifying x + 0.2795918368 = 1.455674387 Reorder the terms: 0.2795918368 + x = 1.455674387 Solving 0.2795918368 + x = 1.455674387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2795918368' to each side of the equation. 0.2795918368 + -0.2795918368 + x = 1.455674387 + -0.2795918368 Combine like terms: 0.2795918368 + -0.2795918368 = 0.0000000000 0.0000000000 + x = 1.455674387 + -0.2795918368 x = 1.455674387 + -0.2795918368 Combine like terms: 1.455674387 + -0.2795918368 = 1.1760825502 x = 1.1760825502 Simplifying x = 1.1760825502Subproblem 2
x + 0.2795918368 = -1.455674387 Simplifying x + 0.2795918368 = -1.455674387 Reorder the terms: 0.2795918368 + x = -1.455674387 Solving 0.2795918368 + x = -1.455674387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2795918368' to each side of the equation. 0.2795918368 + -0.2795918368 + x = -1.455674387 + -0.2795918368 Combine like terms: 0.2795918368 + -0.2795918368 = 0.0000000000 0.0000000000 + x = -1.455674387 + -0.2795918368 x = -1.455674387 + -0.2795918368 Combine like terms: -1.455674387 + -0.2795918368 = -1.7352662238 x = -1.7352662238 Simplifying x = -1.7352662238Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1760825502, -1.7352662238}
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