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Simplifying 7.63x2 + 2.79x = 5.32 Reorder the terms: 2.79x + 7.63x2 = 5.32 Solving 2.79x + 7.63x2 = 5.32 Solving for variable 'x'. Reorder the terms: -5.32 + 2.79x + 7.63x2 = 5.32 + -5.32 Combine like terms: 5.32 + -5.32 = 0.00 -5.32 + 2.79x + 7.63x2 = 0.00 Begin completing the square. Divide all terms by 7.63 the coefficient of the squared term: Divide each side by '7.63'. -0.6972477064 + 0.3656618611x + x2 = 0 Move the constant term to the right: Add '0.6972477064' to each side of the equation. -0.6972477064 + 0.3656618611x + 0.6972477064 + x2 = 0 + 0.6972477064 Reorder the terms: -0.6972477064 + 0.6972477064 + 0.3656618611x + x2 = 0 + 0.6972477064 Combine like terms: -0.6972477064 + 0.6972477064 = 0.0000000000 0.0000000000 + 0.3656618611x + x2 = 0 + 0.6972477064 0.3656618611x + x2 = 0 + 0.6972477064 Combine like terms: 0 + 0.6972477064 = 0.6972477064 0.3656618611x + x2 = 0.6972477064 The x term is 0.3656618611x. Take half its coefficient (0.1828309306). Square it (0.03342714918) and add it to both sides. Add '0.03342714918' to each side of the equation. 0.3656618611x + 0.03342714918 + x2 = 0.6972477064 + 0.03342714918 Reorder the terms: 0.03342714918 + 0.3656618611x + x2 = 0.6972477064 + 0.03342714918 Combine like terms: 0.6972477064 + 0.03342714918 = 0.73067485558 0.03342714918 + 0.3656618611x + x2 = 0.73067485558 Factor a perfect square on the left side: (x + 0.1828309306)(x + 0.1828309306) = 0.73067485558 Calculate the square root of the right side: 0.854795213 Break this problem into two subproblems by setting (x + 0.1828309306) equal to 0.854795213 and -0.854795213.Subproblem 1
x + 0.1828309306 = 0.854795213 Simplifying x + 0.1828309306 = 0.854795213 Reorder the terms: 0.1828309306 + x = 0.854795213 Solving 0.1828309306 + x = 0.854795213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1828309306' to each side of the equation. 0.1828309306 + -0.1828309306 + x = 0.854795213 + -0.1828309306 Combine like terms: 0.1828309306 + -0.1828309306 = 0.0000000000 0.0000000000 + x = 0.854795213 + -0.1828309306 x = 0.854795213 + -0.1828309306 Combine like terms: 0.854795213 + -0.1828309306 = 0.6719642824 x = 0.6719642824 Simplifying x = 0.6719642824Subproblem 2
x + 0.1828309306 = -0.854795213 Simplifying x + 0.1828309306 = -0.854795213 Reorder the terms: 0.1828309306 + x = -0.854795213 Solving 0.1828309306 + x = -0.854795213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1828309306' to each side of the equation. 0.1828309306 + -0.1828309306 + x = -0.854795213 + -0.1828309306 Combine like terms: 0.1828309306 + -0.1828309306 = 0.0000000000 0.0000000000 + x = -0.854795213 + -0.1828309306 x = -0.854795213 + -0.1828309306 Combine like terms: -0.854795213 + -0.1828309306 = -1.0376261436 x = -1.0376261436 Simplifying x = -1.0376261436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6719642824, -1.0376261436}
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